MathDB
Equal segments and angles

Source: IGO 2022 Intermediate P1

December 13, 2022
geometry

Problem Statement

Given is a circle ω\omega and a line ℓ\ell tangent to ω\omega at YY. Point XX lies on ℓ\ell to the left of YY. The tangent to ω\omega, perpendicular to ℓ\ell meets ℓ\ell at AA and touches ω\omega at DD. Let BB a point on ℓ\ell, to the right of YY, such that AX=BYAX=BY. The tangent from BB to ω\omega touches the circle at CC. Prove that ∠XDA=∠YDC\angle XDA= \angle YDC.
Note: This is not the official wording (it was just a diagram without any description).
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