Geometry Problem 1277

Elements: Equilateral Triangle, Circumcircle, Externally Tangent Circles, Tangent Line, Measurement

Circles O and O₁ are tangent externally at T, as shown in the figure. An equilateral triangle ABC is inscribed in the circle O so that T is on the arc BC. If AA₁, BB₁, and CC₁ are tangent to the circle O₁, prove that AA₁ = BB₁ +CC_1.

See also:
Geometry problem 1271 in motion. 

---