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locus of tangency points as center moves

Source: Serbia 2003 1st Grade P4

May 12, 2021
geometryLocus

Problem Statement

An acute angle with the vertex OO and the rays Op1Op_1 and Op2Op_2 is given in a plane. Let k1k_1 be a circle with the center on Op1Op_1 which is tangent to Op2Op_2. Let k2k_2 be the circle that is tangent to both rays Op1Op_1 and Op2Op_2 and to the circle k1k_1 from outside. Find the locus of tangency points of k1k_1 and k2k_2 when center of k1k_1 moves along the ray Op1Op_1.
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