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Tangent Circles

Source:

March 9, 2008
trigonometryHMMTHarvardcollegeMITtrig identitiesgeometry

Problem Statement

Let C1 C_1 and C2 C_2 be externally tangent circles with radius 2 and 3, respectively. Let C3 C_3 be a circle internally tangent to both C1 C_1 and C2 C_2 at points A A and B B, respectively. The tangents to C3 C_3 at A A and B B meet at T T, and TA \equal{} 4. Determine the radius of C3 C_3.
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