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Easy geometry

Source: Lithuanian TST 2014 #1

April 20, 2014
geometryinradiustrapezoidperpendicular bisectorgeometry proposed

Problem Statement

Circle touches parallelogram‘s ABCDABCD borders AB,BCAB, BC and CDCD respectively at points K,LK, L and MM. Perpendicular is drawn from vertex CC to ABAB . Prove, that the line KLKL divides this perpendicular into two equal parts (with the same length).
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