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Exsimilicenters are collinear

Source: 2024 Israel TST Test 3 P1

January 29, 2024
geometryTangentsAngle Bisectors

Problem Statement

Let ABCABC be a triangle and let DD be a point on BCBC so that ADAD bisects the angle ∠BAC\angle BAC. The common tangents of the circles (BAD)(BAD), (CAD)(CAD) meet at the point A′A'. The points B′B', C′C' are defined similarly. Show that A′A', B′B', C′C' are collinear.
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