Proof of the Circle Theorems

Proving the Circle Theorems: the proof that an angle in a semi circle is 90 degrees' the proof that the angle at the centre is twice the angle at the circumference, the proof that angles in the same segment are equal, the proof that opposite angles in a cyclic quadrilateral add to 180 degrees and the proof of the alternate segment theorem.

[helalahmed]

I am speechless, This guy is a pure genius. Thanks a lot sir. You are helping us to get better in maths

[panashe_]

8:14 There is a slight high pitched sound at the end of when he says "degrees"

[petrockspiracy]

Had to watch the last one through about four times but I think I've got it now.

[paulastreet]

@14:09 could you have included the step where you expanded out 1/2(360-x), just for slow thinkers like me ? 😅. Really enjoying trying to get these proofs by myself by pausing the video and having a go!

[paulastreet]

For the fourth proof (the proof that opposite angles in a cyclic quadrilateral add to 180 degrees) I'm not sure how you know which centre angle you use (i.e. x or 360-x). Except that when I turn it upside-down, I can see how 360-x would be the angle to compare with ABD....so, having done that, it's obviously true that the other centre angle must belong to the opposite angle to the one I 'got'!

[MANTRA_OPX]

This is redundancy, you can say simply that BCA=y+x
But A+B+C=180 degrees
Then C+C=180
:C=90degrees
That's it

[Jaffacakemf]

This is fr so helpful I ignored circle theorems like all year and now my paper 2 is in less than a week lol

[LightYagami]

for the first proof, can I say ACB is at the circumference and angle AOB is at the centre while it is 180 degrees. If I use angle at the centre is twice as angle at the circumference, then angle ACB is half of 180 which is 90 degrees and it is a right angle.

[Ahmedhassan-rqny]

wouldnt you say for q1 that angle opposite the diameter = 90

[nighttrain]

Your method for number one uses a circle theorem for its proof; two radii form an isosceles triangle. I though we weren't supposed to use circle theorems to prove circle theorems unless instructed? I've very confused how to answer #1 properly now.

[qaisbaraki]

Just suggestion mathsgenie when you do video please go through the complex stuff aswell

[helalahmed]

When are you gonna make face reveal video?

[paulastreet]

For the last proof, I had paused the video a couple of times and ALMOST got there (I got to the point of realising that it was about angles in a triangle adding up to 180) - but I took so long that I forgot that the question asked for proof re angle ABC!