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prove that the external tangents to AEB and AED meet on AEC

Source: Sharygin Finals 2023 10.6

August 2, 2023
geometrySharygin Geometry OlympiadSharygin 2023

Problem Statement

Let EE be the projection of the vertex CC of a rectangle ABCDABCD to the diagonal BDBD. Prove that the common external tangents to the circles AEBAEB and AEDAED meet on the circle AECAEC.
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