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if |DE| =|BC|, find angle <BAC, perpendicular - circumcircle

Source: Irmo 2015 p2 q8

September 16, 2018
geometryperpendicularcircumcircle

Problem Statement

In triangle △ABC\triangle ABC, the angle ∠BAC\angle BAC is less than 90o90^o. The perpendiculars from CC on ABAB and from BB on ACAC intersect the circumcircle of △ABC\triangle ABC again at DD and EE respectively. If ∣DE∣=∣BC∣|DE| =|BC|, find the measure of the angle ∠BAC\angle BAC.
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