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4.

Part of 2023 Polish Junior MO Second Round

Problems(1)

Geometry with parallelogram

Source: Polish Junior Math Olympiad 2023 Second Stage

5/14/2023
Consider a parallelogram ABCDABCD where AB>ADAB>AD. Let XX and YY, distinct from BB, be points on the ray BD→BD^\rightarrow such that CX=CBCX=CB and AY=ABAY=AB. Prove that DX=DYDX=DY. Note: The notation BD→BD^\rightarrow denotes the ray originating from point BB passing through point DD.
geometryparallelogram