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triangle of incenter and 2 excenters is similar to original triangle

Source: Brazilian Mathematical Olympiad 1982 P1

July 27, 2018
geometryincenterexcenterssimilar triangles

Problem Statement

The angles of the triangle ABCABC satisfy ∠A/∠C=∠B/∠A=2\angle A / \angle C = \angle B / \angle A = 2. The incenter is O.K,LO. K, L are the excenters of the excircles opposite BB and AA respectively. Show that triangles ABCABC and OKLOKL are similar.
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