# Geometry Problem 1434

# Geometry Problem 1434: Equilateral Triangle, Tangent Circles, Tangent Lines,
Arithmetic Mean,
Measurement

### Proposition

The figure shows an equilateral triangle ABC inscribed in a circle O.
Circle O_{1} is tangent to AC at D, arc AB at E, and BM at M. Circle O_{2} is tangent to AC
at F,
arc BC at G, and BN at N. Prove that DF is the arithmetic mean of BM and
BN: BM + BN = 2(DF)

See solution below

### Geometric Art using iPad or Mobile Apps

Geometric art is a form of art based on the use and application of geometric figures. A geometric figure is any set or combination of points, lines, surfaces and solids.

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