Geometry task with lots of circles...
Given an acute triangle PQR. Point M is the incenter of this triangle. A circle omega passes through point M and is tangent to line QR at point R. The ray QM intersects ω at point S≠M.. The ray QP intersects the circumcircle of triangle PSM at point T≠P, lying outside segment QP. Prove that lines ST and PM intersect at a point lying on omega
I got this question and it looks like some angles rush because we know MPTS lay on the same circle but i dont have any more ideas... I though it would come in handy proving that some of the points lay on the same circle, i also had an idea of bashing it but it feels like this method wont work... here is the visualisation of this task cause even drawing this is kinda hard
Posted Oct 11, 2025, 7:47 PM UTC
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