Circle Geometry Example Question (worked proof)

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[@bradirv]

sin(90)st!

[@luisisaurio]

[@ientonghien5941]

(i) arcED= arc CE => angle CDE= angle DCE (Inscribed angle) (1) have: EOD is central angle (2) from (1), (2), we have angle EOD=2x (ii) from (i) we have : ECD is isosceles triangle(3) also have: E is the midpoint of arc CD(4) from (3),(4) we have EQ is perpendicular to CD => angle OQR=angle RPO= 90 conclude: OPRQ is a cyclic quadrilateral.

[@shengshu3510]

I want more of this lol

[@ientonghien5941]

inbox for more

[@williamnguyen2302]

Please do more questions like these I really struggle with this type of questions

[@menachemsalomon]

If all we need to prove is that

[@zolt5626]

I had no idea what he was talking about.

[@dawnelysabeth]

for the second question,, is there a way to prove that the sum of the remaining two angles of the cyclic quadrilateral is equivalent to 180°? also, is it possible to find their values with the information given?

[@ivanhenrickdepedro8176]

Wow!!

[@kuchoomahva1498]

O my dear, you are really great. Thanks a lot.

[@ConTejasMusic]

Could you also have used the supplementary angles theorem for part ii?

[@sparklelight]

great sharing thank you 🌷

[@ivanhenrickdepedro8176]

More of these videos!It is really interesting.📖📚📒🔭📓📒

[@alexismadrid2062]

Great video

[@Κωνσταντίνος-ν7υ]

500000!!!! Congratulations!!!

[@aromeran]

Also useful for my arc drawing test

[@particleonazock2246]

Yep, they throw a whole lot of information at you. Especially at James Ruse where the Year 10 exams are like pi^2 times harder than the average school's.

[@whattt175]

honestly

[@kuchoomahva1498]

In India we have to study such questions a lot.

[@loganv0410]

Correct me, but: arcCE = arcDE therefore line-segmentCE = line-segmentDE therefore triangleCDE is isosceles therefore angleCDE = angleDCE = x degrees therefore angleEOD = 2x degrees because angle at center = twice angle at circumference

[@ishworbasyal7368]

You are correct as well. But why go the long route when you have a short route. In fact, in mathematics and specially in geometry, we can provide various proofs for a same thing.

[@JCW7100]

Love your videos!

[@shubhamtikaria]

First viewer

[@ThePron8]

is this a middle school exam?

[@sophiebobb4010]

Probably about Australian year 10 (because for some reason we leave circle geometry until late high school) so whatever your equivalent of that is lol

[@claudiofelleca4930]

Hi, what kind of software are you using?

[@vitzal3691]

I'm not too sure but I think it's oneNote. I think he has a pen or he's using his finger to draw lines like that on his surface pro because it's touch screen.

[@pranavshyams]

it should be apple pencil and ipad pro if im not wrong

[@sophiebobb4010]

I'm guessing he's using his finger though (definitely not a drawing tablet or anything) because otherwise he'd be quicker and better when writing

[@ishworbasyal7368]

I dont think this is high school exam. I mean that question was too easy. It just included properties of isosceles triangle, some axioms on circle and manipulation of angles. I thought you taught to high school students'.

[@TheMethClub]

Funny Moments This is a high school exam question. I know this because I’m a year 11 student at a school in Melbourne and circle geometry was on the semester one specialist maths exam

[@shawnmcsorley8601]

Its over here in WA aswell

[@richardtrager7125]

shawn mcsorley it’s all over the world actually

[@shawnmcsorley8601]

seems legit

[@ishworbasyal7368]

Oops than my bad...