Let ABC be an acute triangle with AC>AB and circumcircle Γ. The tangent from A
to Γ intersects BC at T. Let M be the midpoint of BC and let R be the reflection of A in B.
Let S be a point so that SABT is a parallelogram and finally let P be a point on line SB such
that MP is parallel to AB.
Given that P lies on Γ, prove that the circumcircle of △STR is tangent to line AC.Proposed by Sam Bealing, United Kingdom Balkanshortlist2021geometryreflectionparallel