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reflection of P in the line QR lies on the circumcircle of the triangle

Source: 1949 Hungary - Kürschák Competition p2

October 9, 2022
geometrycircumcircle

Problem Statement

PP is a point on the base of an isosceles triangle. Lines parallel to the sides through PP meet the sides at QQ and RR. Show that the reflection of PP in the line QRQR lies on the circumcircle of the triangle.
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