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CQRP # if ABR, CBP, ACQ right isoscleles,

Source: 2001 Austria Beginners' Competition p4

October 4, 2022
geometryparallelogramisosceles right triangle

Problem Statement

Let ABCABC be a triangle whose angles α=∠CAB\alpha=\angle CAB and β=∠CBA\beta=\angle CBA are greater than 45∘45^{\circ}. Above the side ABAB a right isosceles triangle ABRABR is constructed with ABAB as the hypotenuse, such that RR is inside the triangle ABCABC. Analogously we construct above the sides BCBC and ACAC the right isosceles triangles CBPCBP and ACQACQ, right at PP and in QQ, but with these outside the triangle ABCABC. Prove that CQRPCQRP is a parallelogram.
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