MathDB
Line through incenter tangent to a circle

Source: Indian TST D1 P1

July 17, 2019
geometryincenter

Problem Statement

In an acute angled triangle ABCABC with AB<ACAB < AC, let II denote the incenter and MM the midpoint of side BCBC. The line through AA perpendicular to AIAI intersects the tangent from MM to the incircle (different from line BCBC) at a point PP> Show that AIAI is tangent to the circumcircle of triangle MIPMIP.
Proposed by Tejaswi Navilarekallu