Competition problem — Geometry — Maths Olympiad Prep

Library / /217 of 520

Geometry Difficulty 5.4 AIME, harder Prove it

187. Given three pairwise intersecting circles. Prove that the three common chords of these circles pass through one point.

Solution

187. Apply the condition proved in problem 173, taking points $A, B$ and $C$ as the centers of the circles, and points $A_{1}, B_{1}, C_{1}$ as one of the intersection points of the circles ( $A_{1}$ - one of the intersection points of the circles with centers $B$ and $C$ and so on.)

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Source: NuminaMath-1.5, licensed Apache-2.0. Statement and solution reproduced as published; topic and difficulty added by this site.