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
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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.