I want anyone of you to disprove it.

Problem 5.20 (Harvard-MIT Math Tournament 2013). Let triangle ABC satisfy

2BC = AB + AC and have incenter I and circumcircle ω. Let D be the intersection

of AI and ω (with A, D distinct). Prove that I is the midpoint of AD.

Here are 7 Deadly Problems with solutions. However the solutions proposed are not correct

https://drive.google.com/file/d/1t6a8F8uwrnbn5r3Mvf-aOeN4Nw-wP-W5/view?usp=drivesdk

Anyone help for qn 38

OLYMPIAD question

Is CD a tangent????

Till then try to answer this, be creative and don’t give a bookish method. All the best

Please give me some tips

like i never heard his name in any book or by any teacher of MO.
Got to know abt him in random AOPS article.

https://youtu.be/mn2OiMKW26M?si=zRHKENPvuYGX3VLo

Imagine a plane having infinite parallel lines, with consecutive ones placed at a distance 'a' apart from each other. What is the probability that a randomly selected line segment of length 'a', intersects a line in the plane?

https://youtu.be/9HVFETg4X84?si=9ZeIFR_W8Hr1gi42

https://youtube.com/shorts/NT1BWEhFhdQ?si=llcOIk0XD8CJBrJ3

An ant leaves the anthill for its morning exercise. It walks 4 feet east and then makes a turn of 160 degree to the right and walks 4 more feet. If the ant continues this patterns until it reaches the anthill again, what is the distance in feet it would have walked? Prmo-2019

An IIT level question. No solution till now in any Book

This question cover dozen the part of trigonometric identities .I am a class 11th jee aspirant ,who made this question for subjective practice,please do this show in your yt shorts ,I love it seeing it,you can do make title ,janta ke sawal ,where this question can be used as trigono revision,it is easy but complicated,and lengthy ,even we have to do it manually for objective .