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BMT 2015 Spring - Geometry P2

Source:

December 30, 2021
geometry

Problem Statement

Suppose that fixed circle C1C_1 with radius a>0a > 0 is tangent to the fixed line ℓ\ell at AA. Variable circle C2C_2, with center XX, is externally tangent to C1C_1 at B≠AB \ne A and ℓ\ell at CC. Prove that the set of all XX is a parabola minus a point
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