LET ABC BE AN ACUTE TRIANGLE, AND ITS ALTITUDES AX, BY, CZ CONCURRE...

2. Let ABC be an acute triangle, and its altitudes AX, BY, CZ concurrent at H. Construct circles

(K

a

), (K

b

), (K

c

) circumscribing the triangles AY Z, BZX , CXY . Construct a circle (K) that

is internally tangent to all the three circles (K

^a

), (K

^b

), (K

^c

). Prove that (K) is tangent to the

circumcircle (O) of the triangle ABC .

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