The 5 Hardest Circle Theorem Exam Style Questions | GCSE Maths Tutor

A video revising the techniques and strategies for answering exam style questions on circle theorems (Higher Only).
This video is part of the Geometry module for Circle Theorems in GCSE maths, see my other videos below to continue with the series.
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Don’t forget to check these videos out:
Part 1 - The Entire GCSE in Only 2 Hours!! Higher and Foundation Revision | GCSE Maths Tutor - • Everything You Need To...
Part 2 - Everything you need for a Grade 6-9 in your Maths GCSE (Higher Only) - • Everything for a Grade...
The 10 Hardest GCSE Maths Questions & How to Solve Them | Grade 9 Maths Series | GCSE Maths Tutor - • The 10 Hardest GCSE Ma...
🔹 Watch the video
🔹 Make notes
🔹 Practice the questions
🔹 Mark your work
🔹 Review what you have learnt on the exam questions
Part 1 - All of the Circle Theorems in 10 minutes! - • All of the Circle Theo...
Part 2 - Circle Theorems - • Circle Theorems - Exam...
Part 3 - Circle Theorems using Algebra - Coming Soon!
Part 4 - Proving the Circle Theorems - • Proving the Circle The...
Part 5 - The 5 Hardest Circle Theorem Exam Questions - • The 5 Hardest Circle T...
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[@someone...000]

For those highly able students aiming for a grade 9 in maths, and not really sure of what to do: well ur at the right place. Watch all of his top hardest gcse question videos, and im ngl ur basically guaranteed that 9! Try to work through all of the problems urself before u watch his solutions, and for each video, try to spot the pattern, as usually these trickier grade 9 questions will have certain patterns as per topic, which if u can spot and acknowledge will massively help u figure out how to approach the exam question whatever it may be! Good luck to all watching and wish everyone a grade 9!

[@raflk6947]

cheers someone

[@user-gg8wz9yy7x]

I got moved into a higher set because of how helpful your youtube channel was, thank you so much!

[@TheGCSEMathsTutor]

Wow that is incredible!!! Well done for being so committed that’s an awesome achievement 👏🏼👏🏼

[@oscillatefn8303]

Nicee bro 💯🔥💪🙌👍👏🏅🥇🏆🌟🙏👏💰💰💰😁🙏👏

[@kirtip3605]

Well done

[@rayhaan7860]

same bro

[@lainexxx]

sameee now I’m so happy I’m doing higher maths

[@_liampitigala_1796]

You sir, have made me motivated for my math GCSE's. Please sir make a math website. You're so underrated, i'm going to shout your name in my math GCSE exam for you

[@TheGCSEMathsTutor]

Amazing news! So glad to hear that 😁🙏🏼 I have made a website but it’s very much a work in progress still it’s www.thegcsemathstutor.co.uk/ it’s still got a lot of updates to make but it’s getting there 😁🤞🏼

[@aaryanramani1699]

@@TheGCSEMathsTutor Nice Website

[@oliviaaa2324]

listen to me i have literally based my whole gcse revision on your videos. ong you are so underrated and take my word when I say you're gonna blow up very fast very soon. thank you so much we all appreciate you.

[@Aman-ge1tp]

Calm down Olivia I’m pretty sure he is married. 😂😂

[@oliviaaa2324]

@@Aman-ge1tp lmao I never meant it like that

[@xhibah]

@@Aman-ge1tp that’s a shame, i’m turning 18 in 3 years 😔😂

[@paperlytical8067]

These videos are amazing! They've helped me understand maths at TON!!! Because of these videos, I've improved from 4s to 7s for EDEXEl and its all thanks to you.

[@Ryan-bm8lc]

i initially understood none of these but you explain it so fluently in such an easy-to-understand way that i understand how to do it almost instantly

[@alisha3771]

i honestly can't thank you enough for these videos you literally saved my maths gcses. thank you so much for making these lessons free as well thats really useful

[@numskulll]

Nice problems! Some alternative approaches to consider: Q1: ACB = 56 deg (alternate segment); CBO + CAO = ACB (due to isosceles triangles CBO and CAO), hence CAO = 21 deg Q4: BOC = OBA + OAB (external angle of a triangle) Q5: y = BAD = BDE (alternate segment) = = x + 90 deg, hence y - x = 90 deg

[@numskulll]

Solution 2: after getting the 25 degree angle (at 9m:06s), just use cyclic quadrilateral to get BCD = 180 - 25 = 155.

[@niveankoneswaran7395]

It's so much easier to understand when you explain it. Thank You!

[@user-ny4ho4ku1h]

I like how you explain , step by step getting to a solution. Thank you .

[@anjanaajmera7207]

In the first qs, u could have directly gotten angle BCA as 56 from the alternate segment theorem, and angle OCA would've become 56-35=21. Triangle OCA is iscoceles hence angle CAO=21. simple. cheers

[@kuhinde]

this is genuinely so helpful

[@mohammadtaosif]

I just want to say thank you. These videos are super helpful!

[@TheGCSEMathsTutor]

Amazing news! So glad to hear it’s useful 😁🙏🏼

[@PsychRightyt]

Really helpful as I have a test on this in a week - amazing work👍

[@TheGCSEMathsTutor]

Amazing news! Best of luck 😁🤞🏼🤞🏼

[@GCSEALevelMaths]

Very useful sir hope you’re well too work. Happy half term!!

[@MKhan-qe9lp]

great video. geometry is a tad difficult but you know your stuff.cheers for this.

[@TheGCSEMathsTutor]

Thank you! I think geometry tends to be one that is taught less frequently and tends to be found more difficult for this reason, lots of practice and you’ll ace it 😁🙏🏼🙏🏼

[@muhammadaizaz2233]

This teacher is legend. Best teacher ever. Thank u very very very much

[@TheGCSEMathsTutor]

Thank you so much for the kind words!!!

[@turtleboy3628]

Great video ty

[@shins_clips]

This is what I was looking for! Like and subbed

[@TheGCSEMathsTutor]

Amazing news! So glad to hear that you have found what you were looking for! :-)

[@Mathspaperks1ks2]

Really nicely explained video congrats on surpassing 58k!! You have surpassed TLmaths and he's a big KZbinr as well!! Nice one sir!! Keep grinding!!

[@TheGCSEMathsTutor]

Thank you 😁🙏🏼🙏🏼

[@trumpgaming5998]

This video helped SO much thank you.

[@TheGCSEMathsTutor]

So glad to hear that! 😁🙏🏼🙏🏼

[@roxers8700]

For the thrid one @The GCSE Maths Tutor, u could use sine rule

[@hellofriends5662]

also, at 9:07, when you drew those extra lines, that turned it into a cyclic quad which means that 25 + x = 180 to solve for x if that makes things easier

[@Masowe.]

thank you sir. i moved from grade 6 now 1 mar away from grade 9 with your videos and 1 week away from exams but i want a 9

[@TheGCSEMathsTutor]

Wow!!!! That is incredible congratulations to you! So glad to hear the channel is helping so much 😁🙏🏼🙏🏼🙏🏼

[@Masowe.]

@@TheGCSEMathsTutor thank you so much for appreciation. I want to kill the exam

[@not_today_x]

Last Question alternative method (lmk if im wrong lmao)

[@areebahaque5916]

A life saver💝💝💝

[@patoneill4348]

Really helpful 👍 Can u make one video for area of a compound shape ? Please 🙂

[@pyrite2060]

for the last question, i would just call angles ABD, ADB and FDA "a", form the equations 2a + y = 180, and 2a + x = 90, and then minus them from one another

[@calcpost3641]

Hi Sir, do you hve a document containing these questions to print, because i find it difficult to complete circle theorems without the diagram.

[@turbiyo4026]

I got a simpler answer for the last question (Angle BDE)=x+90, which is equal to y( because angles in alternate segments are equal) Then we have, x+90=y And then simply rearrange to give,90=y-x

[@TheGCSEMathsTutor]

Love it! All part of the beauty with circle theorems 😁🙏🏼

[@neverosman]

thanks bro

[@sethumuthaiah1363]

bro this helped so much ty

[@TheGCSEMathsTutor]

No problem at all! Glad to hear it 😁🙏🏼

[@safahussain5234]

Could you put a pdf version in the description so I can print it out. I think this would be useful for many people

[@ayeeeeee178]

CAN U PLEASEEEE MAKE VIDEOS ON MENSURATION PROBLEMS???😭😭🙏 you are a life saviour

[@dong1971]

In the last question we know that BAD is an alternate segment angle to BDE. So BAD = BDE. BDE = 90 + x. Hence, y = 90 + x. Re arranging y - x = 90.

[@ultimaterevision437]

Brilliant video :)

[@TheGCSEMathsTutor]

Amazing news! Thank you 😁🙏🏼🙏🏼

[@St-jh8pk]

Thank you, this is a very useful and informative video! 😊

[@TheGCSEMathsTutor]

So glad to hear it! What topics will you be looking at next? 😁🙏🏼

[@St-jh8pk]

👍I think I will be looking at more circle theorems then graphs 📉

[@TheGCSEMathsTutor]

@S t Amazing news! Let me know how you get on with them 😁

[@St-jh8pk]

@@TheGCSEMathsTutor Thank you! I will do 😀

[@wowigcses]

In the third question, the one which has an answer of 21.6cm, I don't get why you wouldn't do the arrowhead method? If we drew a line from A to B and another from C to B, we would get the arrowhead shape and half the angle COA (112.5...) which would give us an answer of 56.3cm to 3 sf. I understand you can't assume that it's an arrowhead but the video did at 8:56. Any help is appreciated!

[@andrik_1312]

Is it alright for question 2 to draw arrow shape, so that the angle at the circumference is 25; then we see that it forms a cyclic quadrilateral, so that angle x = 180 - 25 = 155.

[@omarkrubally8071]

what a legend thank you

[@TheGCSEMathsTutor]

No problem at all! 😁🙏🏼

[@meritayo6336]

Exam questions per unit / gcse formula videos?

[@user-ny4ho4ku1h]

Can you also post trigonometry please.

[@ohhhmyyylifeee]

dont understand how the number 310 on that side of the arrow head relates to BCD. what rule does he use for this? At 9:43. Thx

[@CobraMindset302]

Hi , you know the second questions , which Gcse paper is it from ? Thank you

[@sabinelehmann3443]

Hi! For question 4 shouldn't you divide the 90 - 2x by 2 to get 45 - x because the question says to leave your answer in its simplest form? Btw thanks so much, your videos are beyond helpful and I love the way you explain things:)

[@darkrebel5520]

Hi Sabine - you can't do that with an expression (a bit of algebra with no "=" signs) - for example, lets hypothetically say x = 10. Using that we get that 90-2x is 70, but 45 - x is 35. It gives us a completely different answer. Hope this helps

[@mirshathmohamed2814]

4:12 for that angle that was 56 degrees, can you not just do the alternate segment/angle theorem?

[@theotheoth]

19:24 At this stage of question 4, it is already obvious that that triangle ABC has angle BAC = x, and angle ABC = 90 + x, so angle ACB = 180 - x - (90 + x). There is no need to work out the algebra on the straight line for angles AOB and COB. (I'm sure someone must already have pointed this out below.)

[@NishilK]

at 13:54, why is it cos-1 and not just cos?

[@enda2658]

For Q4, is 90 -2x the simplest form? Should you divide by 2 = 45 - x

[@HelloHi-pl4zk]

No because 90-2x=angle ACB, so if you divide the left by 2 u just divide the right by 2 as-well, Meaning 45-x=ACB/2, which is not the same as ACB so it is not simplified

[@rainycypher1761]

q 2 9:13 would it be possible to use the cyclic quadrilateral supplementary angle rule

[@bigmanzain240]

no because not all angles are touching the circumfrence hence making it not a cyclic quadrilateral

[@axdux_rl50]

Ian confused on that first one. After u got 34 i thought u would do base angles are the same in a equilateral so i tried to do 56 - 34 = 22 but i guess that’s not right

[@Grizzly01]

There aren't any equilateral triangles present in the question.

[@harisamaan786]

If you know how to do these circle theorem questions will i be confident with circle theorems?

[@TheGCSEMathsTutor]

I would say so absolutely! Always check other questions along the way on past papers still though 😁🙏🏼

[@bilalhussain6417]

What do you think I should do to get a higher grade in maths I’m a current grade 4 but I would like a 7 , my mocks are in 4 weeks

[@TheGCSEMathsTutor]

I would work through the grade 5 crossover playlist straight away, get yourself confident with those topics and then you can move onto the grade 7 playlist. But mastering the topics in the grade 5 playlist needs to be a priority 😁🙏🏼🙏🏼

[@bilalhussain6417]

@@TheGCSEMathsTutor Does this cover every topic in grade 5 or only grade 5 topics ? And What topics are mostly end questions in the papers ? (P1,2,3)

[@TheGCSEMathsTutor]

@@bilalhussain6417 pretty much! It’s 99% complete I just have a few extras to add in soon! In terms of the end questions please see the grade 9 playlist 😁🙏🏼🙏🏼

[@bilalhussain6417]

@@TheGCSEMathsTutor do you know which topics your missing 🙏 . I got to revise maths before my mocks which is real soon

[@TheGCSEMathsTutor]

@@bilalhussain6417 Constructions and Loci 😁🙏🏼🙏🏼

[@_GOBLIN1]

how many marks wuld these be

[@shehreenrana3913]

can we not write 90+2x-180=acb? for question at 20:46

[@Grizzly01]

No, that wouldn't be in the correct order, so would give you a wrong answer. You'd end up with 2x - 90 ∠ABC = 180 - (90 + 2x) = 180 - 90 - 2x = 90 - 2x

[@hughmacwhirter2653]

Less go

[@calcpost3641]

Sir at 9:48 how would you have identified that it was that specific circle theorem

[@cali5635]

the angle subtended at the centre is twice the size of the angle subtended at the circumference

[@criticalthinker-vw2yy]

hi sir, the question at 16:53 time stamp, why did you use the angle of 247.49 instead of 112.502. Thank you in advance. Your videos have honestly been so helpful

[@nomanchaudry2494]

He did that because he had to find the length of the arc ABC, and in order to do that he had to find the angle within that shape to use in the formula: pi x diameter x angle/360. He got the angle of 247.49 by subtracting it from 360, as there are 360 degrees in an angle around a point(known as a reflex angle). As the angle at the bottom of triangle ACD was 112.502, he did 360 - 112.502 to get that angle of O(247.49) in order to substitute that into his formula to work out the arc length

[@criticalthinker-vw2yy]

@@nomanchaudry2494 thank you very much noman

[@nomanchaudry2494]

@@criticalthinker-vw2yy no problem

[@urrnothim]

Q2 also has the cyclic quadrilateral when u done 25 degrees, so could have done 180-25 = 155

[@TheGCSEMathsTutor]

Absolutely! The beautiful thing about circle theorems is the different approaches that you can take 😁🙏🏼

[@user-kc3fw9gm2j]

Where's the cyclic quadrilateral?

[@user-kc3fw9gm2j]

If you're talking about BCDO then you're incorrect

[@Grizzly01]

@@user-kc3fw9gm2j the extra lines drawn in at 8:50 to illustrate the inscribed angle theorem. If you label that point created on major arc BD - let's say point E - then BCDE is a cyclic quadrilateral.

[@Bannapickleonion]

so in any question can i draw an isosceles traingle

[@Grizzly01]

Only if you can show that one exists.

[@jodiebeard3816]

LEGEND

[@TheGCSEMathsTutor]

Thank you 😁🙏🏼

[@JH-jv5ru]

For number one couldn’t you just use alternate segment theorem again with 69°(34+35) and then subtract 180° by 69+90= 21??

[@TheGCSEMathsTutor]

The beautiful thing about circle theorems is that there are so many ways to make your way through the question to the final answer! 😁🙏🏼

[@edena3888]

do you have to memorise the arc equation?

[@Grizzly01]

Just remember that it's the circumference formula (2πr) multiplied by whatever fraction of a full circle your angle is (angle/360). Same goes for the area of a segment: it's just the area of a circle formula (πr²) multiplied by whatever fraction of a full circle your angle is (angle/360).

[@calcpost3641]

sir how do we know that 50 isnt the angle at the centre at 9:57

[@Grizzly01]

But it is the angle at the centre.

[@diamond-zb6rl]

Can u do predicted paper for November resit gcse

[@TheGCSEMathsTutor]

I’ll do my best! It is impossible to do a ‘predicted paper’ though but I can do a ‘best guess’ practice paper for sure 😁🙏🏼🙏🏼

[@diamond-zb6rl]

Thank you so much caould u do it as soon as possible as my paper 1 maths exam is on Tuesday 3rd of November!

[@TheGCSEMathsTutor]

@@diamond-zb6rl Check out the series here: kzbin.info/www/bejne/hGHbZGethsSrpdk 😁🙏🏼

[@diamond-zb6rl]

Thanks!

[@Masowe.]

@@diamond-zb6rl me too.

[@IsraaHusam]

in the first question, angle CBO and OBA are facing the same arc why is OBA 34 it should be 35, isn't it?

[@Grizzly01]

If you look again, you'll see that they aren't.

[@jeffnyjesuthas7949]

I'm doing a test on this in less than an hour and the average percent for people that have done this test was around 30%. You have honestly, made me so much more confident than i was this morning when i was absolutely terrified and i hope that because of this video, i will do well. Thank you!!

[@sahityavenkat8787]

I've heard you have a website, it is compulsory that I have to put my email to access the free revision practice questions? I'm sorry I'm really paranoid 😅

[@TheGCSEMathsTutor]

If you don’t want to put your email just set up a new one 😁

[@sahityavenkat8787]

@@TheGCSEMathsTutor oh right, thanks!!

[@Charlotte-yw9eq]

hey there i just came from you’re grade 6-9 whole maths paper video (hope you know which one i’m talking about eek) and i was just wondering after i watch that should i do practice papers and questions because i’ve got mocks in less than a month 😬 and also should i watch both 2 hour vids or just the grade 6-9 one

[@TheGCSEMathsTutor]

Great to hear! I would make sure you watch both, any topics you are unsure of then look at the focus videos on these topics and focus your revision into these areas along with past papers 😁🙏🏼🙏🏼

[@Charlotte-yw9eq]

@@TheGCSEMathsTutor thank you so much ! do you recommend writing notes whilst watching or just watch them

[@TheGCSEMathsTutor]

@@Charlotte-yw9eq Writing notes as an absolute essential unless you are just using it as a reminder 😁🙏🏼

[@TheGCSEMathsTutor]

@@Charlotte-yw9eq Writing notes as an absolute essential unless you are just using it as a reminder 😁🙏🏼

[@INeedGooderGrades]

first 3 too easy for me :)

[@punithankristmehan6193]

I can't believe that a piece of paper is deciding my life......

[@premamuthukumar5352]

13:59 Why is it cos "-1" ?

[@________0001]

we should use cos inverse (cos -1) to find the angles using soh cah toa, if we are trying to find the length of a side we can use normal cos

[@premamuthukumar5352]

@@________0001 thank you!

[@harveersethi2462]

23:00 "and it shez show"

[@amermistarihi3145]

u said ode=y in q5 this incorrect ode is tangent to radius fix it

[@leannelowe5441]

i spotted this one also

[@Grizzly01]

Yeah, he must've got a bit confused there. You could use the alternate segment theorem to show that ∠BDE = y, then knowing that ∠BDE = x + ∠ODE = x + 90° take it from there.

[@mistermusab8055]

9:28

[@herojames4261]

hi

[@ewanathol6347]

Math addict

[@TheGCSEMathsTutor]

The best kind!

[@mrgoatliri6224]

God channel

[@TheGCSEMathsTutor]

Thanks for the kind words!! 😁🙏🏽

[@ttee1397]

Advice for revising for gcse maths

[@TheGCSEMathsTutor]

Work through the playlists on this channel, make lots of notes, do a past paper, whatever you get wrong focus your revision on these topics and then repeat the process 😁🙏🏼

[@tawa1066]

The last one was the easiest one tbh

[@beatsbysin5599]

am i the only one who thinks higher paper is actually easier than foundation

[@memetris6971]

Yes

[@mathsmadefun6484]

no i think that aswell

[@stealt7073]

Yes u are the only one

[@fishymemes2308]

Skill issue

[@j6lkx5kt31]

yes