How to Prove Ptolemy's Theorem for Cyclic Quadrilaterals

[@MuPrimeMath]

Adding the point K on AC is such an interesting step! I hope I can learn how to do geometric proofs like these at some point!

[@ProfOmarMath]

It's an interesting creative step. Maybe too magical!

[@Szynkaa]

there is also slightly extended version of it- namely we have inequality AD*BC+AB*DC>= AC*BD with equality iff quadrilateral is cyclic.

[@myrus5722]

I always love those "magic line" proofs :) -- They really embody the creativity and ingenuity in proof geometry (which is often seen as the boring, rigorous way to do things) that is often missed by those that don't study it as deeply (that can be said for almost all subjects, too). Thank you for this pretty cool proof. There are certainly more beautiful proofs, like the inversion one, but I still really like the approach you took. You seem more into mathematics than a lot of other people I've seen with similar channels... It doesn't feel like you're parroting a website and dryly restating the proof, but actually sharing your love of math with the audience.

[@ProfOmarMath]

Thanks Myrus! I really do love the stuff and wish I could share so much more

[@gardening_vibes]

Thank you for this. I was searching for proof of Ptolemy's theorem.

[@ProfOmarMath]

Definitely!

[@fernandoadrianromeroalvare2612]

Excellent explanation Omar!

[@sumaitarimjhim3926]

thanks very much!! I was really struggling with the proof I have in my book, yours is much easier to absorb.

[@srijaghosh9723]

Thank you sir for explaining in such an easy way 😊🙏

[@atharvagarwal6412]

Loved it! This channel is a gem. Here from blackpenredpen's video :D

[@ProfOmarMath]

Thanks!

[@az8887]

you should do more things like this. I am personally a great fan of planimetry, but sometimes feel a bit too lazy to read the proofs myself.

[@ProfOmarMath]

More coming 😊

[@mike_the_tutor1166]

Excellent video. Thank you for sharing.

[@ProfOmarMath]

Thank you!

[@sathwik5460]

can you please advice me some good book which has angle chasing problems ?

[@ProfOmarMath]

Hmmmm I actually can’t think of a specific outstanding one!

[@DragonKidPlaysMC]

Can you olympiad techniques for euclidean geometry like inversion and barycentric coordinates?

[@ProfOmarMath]

Hi Drag. I typically focus on undergrad math material but I have some interesting techniques that apply to geometry coming quite soon that are quite surprising! Did you think about this from the inversion proof of Ptolemy?

[@krishshah3974]

Noice! A slow clear explanation!

[@ProfOmarMath]

Thanks!

[@rksharma7132]

Cristal clear 👌

[@debarshimukherjee8755]

Sir how did you get the idea to construct the angle bisector? Or you knew it beforehand?

[@ProfOmarMath]

This is indeed something I had seen before!

[@atharavyadav2979]

@@ProfOmarMath plz prove it

[@SeanBenson23]

@@atharavyadav2979 dude it doesn’t need to be proved. You’re allowed the make that construction. Use a protractor and a straightedge.

[@atharavyadav2979]

@@SeanBenson23 my friend i was asking therotical proof . yeah always we can prove it from construction not only that but even ptolmey theorem can proved by construction

[@sathwik5460]

thank you .

[@ProfOmarMath]

Definitely!

[@utkarshkathuria2931]

How can I prove using Complex numbers?

[@TechToppers]

This proof looks like magic. Really. Inversion looks much more intuitive.

[@ProfOmarMath]

Truth. Inversion takes a lot of set up. There is a nice numberphile about it actually

[@TechToppers]

@@ProfOmarMath Yeah. I have a small request. Can you make a video on what's the idea of Circular Inversion, because that definition looks rather strange on first look but solves circle related problems in a jiffy.

[@susancheng4782]

great! thank you! very enlightening!

[@ProfOmarMath]

You're very welcome!

[@SuperYoonHo]

subbed

[@brokelama7191]

Thank you so much for the explanation. :D. It really helped.

[@ProfOmarMath]

Awesome!

[@015_Abdur_Rob]

Which theorem was invented first Pythagoras or Ptolemy??

[@ProfOmarMath]

I'm not sure!

[@hvcreator2380]

THANK U SOO MUCH ❤

[@thequantmentor]

Very good video!! Keep going :)

[@radheya]

Nice explanation

[@ProfOmarMath]

Thanks!

[@王剛-m7n]

Great！ Beautiful！

[@anas8183]

نايس

[@ujjwaldhawan281]

dont knw why good youtubers have so less subs.....

[@ProfOmarMath]

Thanks Ujjwal. Can’t control the algorithm!

[@mrshockgod4476]

good vid

[@ProfOmarMath]

Thanks!

[@yashraj8028]

❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤👍👍👍👍👍👍👍👍👍👍👍👍👍

[@pranshu05]

2:05 Khabi Lame moment