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equal angles wanted, circle tangent to intersecting circles

Source: 239 MO 2001 VIII-IX p5

May 7, 2020
geometrytangent circlescirclesequal angles

Problem Statement

The circles S1 S_1 and S2 S_2 intersect at points A A and B B . Circle S3 S_3 externally touches S1 S_1 and S2 S_2 at points C C and D D respectively. Let K K be the midpoint of the chord cut by the line AB AB on circles S3 S_3 . Prove that ∠CKA=∠DKA \angle CKA = \angle DKA .
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