Question 131
Let $I$ be the incenter of scalene triangle $ABC$ inscribed in circle $\omega$. The line $BI$ intersects $\omega$ again at point $M$. Let $I_B$ be the reflection of point $I$ across line $AC$. Let $H$ be a point on the minor arc $AM$ of $\omega$ such that $\angle BHI_B = 90^\circ$. Let $T$ be the intersection point of lines $II_B$ and $AC$. Let the line $HT$ intersect $\omega$ again at point $N$. Let $R$ be the intersection point of lines $MN$ and $AC$. Prove that triangle $\triangle IRM$ is isosceles.
(Batzorig Undrakh)
(Batzorig Undrakh)