MathDB

AI x IX wanted, 6-8-10 triangle, incenter circumcircle 2020 BMT Team 21

Source:

January 7, 2022

geometryincentercircumcircle

Problem Statement

Let

\vartriangle ABC

be a right triangle with legs

AB = 6

and

AC = 8

. Let

I

be the incenter of

\vartriangle ABC

and

X

be the other intersection of

AI

with the circumcircle of

\vartriangle ABC

. Find

\overline{AI} \cdot \overline{IX}