Superb sir. I expected this chords theorem from you. Thank you for your teaching.

You have such an absorbing way of describing solutions. I find myself hanging on your every word.

This my preferred channel in the whole KZfaq!! You are an excellent teacher! Thanks!

Excellent presentation showing the proof to the intersecting chords theorem. Expertly done and easily verifiable.

Generally, any chord through a fixed point inside a circle, the product of two line segments is a constant, actually equal to the square of radius minus the square of the distance of the point from the center

This is a very clear explanation of the proof of the theorem 👍.

Thank you for posting these lessons.

Thank you. Great teaching, step by step

Good video , easy and simple explanation . Looking fwd for more videos Max - Melbourne - Australia 13th June 22

proofs are wonderful it means one truly understands the problem,. its a great feeling to work proofs. thanks ..

Very clear explanation. Thank you very much!

As angle A and angle C are both on the same side of chord BD and touch the circumference of the circle then they are equal [ or as you say, congruent] . Angle APB = angle CPD as they are vertically opposite angles on intersecting straight lines and thus remaining angles equal [Or as angle B and angle D are on same chord AC the they are equal [proof as before stated. Thus follow proof by by using similar triangle proportion properties for triangle APB and triangle CPD So that AP/PC = BP/PD and rearrange by transposing this to give the proof. (AP)(PD) = (BP)(PC) [QED]

Thank you, professor!!

Beautiful!

Thank you sir for this!

The only difficulty that I had on the topic of naming angles was the use of like sounding letters. The vocalization of angles sounded like a succession of EE's which took a lot of attention in discriminating them. The English alphabet has other letters than though which would help in this regard, e.g. F,M,Q, etc. Tamir's solution would also be good. That said, I liked the video, and your explanation.

Thanks! Very helpful!

I would have preferred a proof that doesn't use other non obvious theorems like the Inscribed Angle Theorem, but just the defining properties of a circle.

Awesome Sir ♥️

Thank you for teaching us 😊

Hallo, actually I have one more method to proof AP*PD=BP*PC. The first step just like you did to proof the similarity of two triangles APB & CPD, then after that you can use "Sine Rule Theorem" applied on those two similar triangles, from here you can get the proof of intersecting chords theorem, that is AP*PD=BP*PC.

More posts on Cords and Circle please…

Bahut badhiya :-)

i watched and liked the video

And now you have to prove the inscribed angle theorem!

Thank you

Thank you sir.

The length of the arc , being of course, measured in radians ?

Good video

Hello sir...pls reply me... My interestin question is Just keep AD line same.. And keep B point just near right to A And keep C point just left to A ... And then Lenght of first line will be long.. And replaced point connected line will be small...then how can be this possible

Can you prove it using coordinate geometry as well?

Very interesting👍👍

Thanks for your efforts. I would like to know the link where I can find all the proofs for Chord, Secant and Tangent of a circle?

Thankyouuuui

i am wondering how it works if C stay on circle couple millimeters from A next?

Super

Nice proof !

Step 4 IS not written properly: Because triangle are similar , u Can write [AP]/[BP]= [CP]/[PD]

Is this theorem true only when both chords have an equal length?

La force d'un point dans le cercle

What is the "reason" for step 4 for a proof table?

Vvnice true thanks

1st view sir

You can't be from the United States

similarlity👍

im still so lost

In the above case the application of the 'Vertical Angles Theorem' has to be explained in context with a circle, that's obvious. Otherwise you cannot prove the 'Intersecting Cords Theorem'. Got it? So the applauding comments of most of your followers are insignificant.

Voice is so irritating