One of the most important properties about excircles

In this video, we present a solution to Iran TST 2015/2.
00:00 Problem Statement
00:41 Solution
Check out our website www.calimath.org to find past problems, solutions and other cool stuff.
Solution PDF: calimath.org/pdf/IranTST2015-...
branch: geometry
difficulty: 7
Our website: www.calimath.org
Contact us: [e-mail]

[@user-kj6lj7dp9j]

wonderful video !

[@calimath6701]

Thanks!

[@Cooososoo]

How do you construct diagrams so perfectly

[@calimath6701]

Just a large compass and ruler and many attempts :D

[@mohammedmarzuqrahman8605]

Why TB × TC = TS^2 ? 3:32

[@calimath6701]

At this point, we haven't proven it; it's just a guess used to motivate the upcoming part of the video. The reason behind the guess is that both I_B and S are intersections of TM with the circle, indicating they should play similar roles. Therefore, if TB × TC = TB_I^2 holds true, then we anticipate TB × TC = TS^2 to be true as well.

[@Mather4269mixti]

You can also prove this using Ib as a circle of radius 0😅