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angle chasing, tangents at circumcircle of a right triangle

Source: China Northern MO 2015 10.2 CNMO

October 28, 2022
geometryanglesdiametercircumcircle

Problem Statement

It is known that ⊙O\odot O is the circumcircle of △ABC\vartriangle ABC wwith diameter ABAB. The tangents of ⊙O\odot O at points BB and CC intersect at PP . The line perpendicular to PAPA at point AA intersects the extension of BCBC at point DD. Extend DPDP at length PE=PBPE = PB. If ∠ADP=40o\angle ADP = 40^o , find the measure of ∠E\angle E.
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