MathDB
Right angles

Source: 2018 Taiwan TST Round 3

April 2, 2020
geometryTaiwan

Problem Statement

Let II be the incenter of triangle ABCABC, and ℓ\ell be the perpendicular bisector of AIAI. Suppose that PP is on the circumcircle of triangle ABCABC, and line APAP and ℓ\ell intersect at point QQ. Point RR is on ℓ\ell such that ∠IPR=90∘\angle IPR = 90^{\circ}.Suppose that line IQIQ and the midsegment of ABCABC that is parallel to BCBC intersect at MM. Show that ∠AMR=90∘\angle AMR = 90^{\circ}
(Note: In a triangle, a line connecting two midpoints is called a midsegment.)
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