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Found problems: 1

1955 Moscow Mathematical Olympiad, 308
Tags: bisect arc , circles , tangent circle , tangent , geometry
* Two circles are tangent to each other externally, and to a third one from the inside. Two common tangents to the first two circles are drawn, one outer and one inner. Prove that the inner tangent divides in halves the arc intercepted by the outer tangent on the third circle.