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Prove that DK = DL

Source: MEMO 2008, Single, Problem 3

September 10, 2008
geometryincenterprojective geometrygeometry unsolved

Problem Statement

Let ABC ABC be an isosceles triangle with AC \equal{} BC. Its incircle touches AB AB in D D and BC BC in E. E. A line distinct of AE AE goes through A A and intersects the incircle in F F and G. G. Line AB AB intersects line EF EF and EG EG in K K and L, L, respectively. Prove that DK \equal{} DL.
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