Online Geometry Problem 885: Three Intersecting Circles, Three Tangent Lines,
Midpoint. Level:
High School, Honors Geometry, College, Mathematics
Education

In the diagram below, the circles A and B intersect at C and
D. CE is tangent to circle A at C, CF is tangent to circle B at C,
circle G passes through the points C, E, F. If HM is tangent to circle G
at C, prove that C is the midpoint of HM.