# Geometry Problem 1435

See solution below

# Geometry Problem 1435: Circle, Diameter, Inscribed Circles, Circular Sector,
Parallelogram, Parallel Lines, Tangency Points

### Proposition

C is a point on a circle O with diameter AB. A circle O_{1} is
inscribed in the circular sector AOC (It is tangent to
OA at D, OC at E, and arc AC at F). A circle O_{2} is inscribed in the circular sector COB (It is tangent to
OC at H, OB at G, and arc BC at K). AC and DF meet at P. BC and GK meet at
M. Prove that (1) PEMH is a parallelogram and (2) PM is parallel to AB.

See solution below

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