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isosceles wanted, starting with two ext. tangent circles

Source: Dutch NMO 2004 p4

September 21, 2019
geometrytangent circlesisosceles

Problem Statement

Two circles C1C_1 and C2C_2 touch each other externally in a point PP. At point C1C_1 there is a point QQ such that the tangent line in QQ at C1C_1 intersects the circle C2C_2 at points AA and BB. The line QPQP still intersects C2C_2 at point CC. Prove that triangle ABCABC is isosceles.
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