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angle chasing , <ECB = 30^o, <FBC = 15^o, right isosceles

Source: 2020 Argentina OMA L3 p3

December 26, 2020
geometryanglesright triangleisosceles

Problem Statement

Let ABCABC be a right isosceles triangle with right angle at AA. Let EE and FF be points on ABB and ACAC respectively such that ∠ECB=30o\angle ECB = 30^o and ∠FBC=15o\angle FBC = 15^o. Lines CECE and BFBF intersect at PP and line APAP intersects side BCBC at DD. Calculate the measure of angle ∠FDC\angle FDC.
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