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Geometry Mathley 6.2 CCC contrsuction, tangent circles

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June 7, 2020
orthocentergeometrytangent circlesconstructioncircles

Problem Statement

Let ABCABC be an acute triangle, and its altitudes AX,BY,CZAX,BY,CZ concurrent at HH. Construct circles (Ka),(Kb),(Kc)(K_a), (K_b), (K_c) circumscribing the triangles AYZ,BZX,CXYAY Z, BZX, CXY . Construct a circle (K)(K) that is internally tangent to all the three circles (Ka),(Kb),(Kc)(Ka), (K_b), (K_c). Prove that (K)(K) is tangent to the circumcircle (O)(O) of the triangle ABCABC.
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