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prove tangent to (ABD) at B bisects EC

Source: Sharygin Finals 2023 9.5

August 2, 2023
geometrySharygin Geometry OlympiadSharygin 2023Isosceles Triangle

Problem Statement

A point DD lie on the lateral side BCBC of an isosceles triangle ABCABC. The ray ADAD meets the line passing through BB and parallel to the base ACAC at point EE. Prove that the tangent to the circumcircle of triangle ABDABD at BB bisects ECEC.