Geometry Problem. Post your solution in the comment box below.

Level: Mathematics Education, High School, Honors Geometry, College.

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## Saturday, March 14, 2015

### Geometry Problem 1098: Circles, Common External Tangent, Common Internal Tangent, Radius, Metric Relations

Labels:
circle,
common tangent,
metric relations,
radius

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Obvious ∠O₁CO₂=90°, thus ∠O₁CA₁ + ∠O₂CA₂=90°.

ReplyDeleteThat is, ΔO₁CA₁~ΔCO₂A₂.

Hence, O₁A₁/CA₂ = CA₁/O₂A₂.

i.e. r₁×r₂ = A₁C×A₂C.