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Feuerbach point in a right angled triangle.

Source: Sharygin Correspondence Round 2024 P14

March 6, 2024
geometry

Problem Statement

The incircle ω\omega of triangle ABCABC, right angled at CC, touches the circumcircle of its medial triangle at point FF. Let OEOE be the tangent to ω\omega from the midpoint OO of the hypotenuse ABAB, distinct from ABAB. Prove that CE=CFCE = CF.
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