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Kissing Right

Author:
John Golden
Topic:
Angles, Circle
From a Brilliant.org problem by Banti Paswan, https://brilliant.org/profile/arron-udsft3/sets/arrons-picks-level-1-challenges-2015-iii/223226/problem/simple-geometry-3/ Why is the triangle formed by the intersection points of two tangent circles and a line tangent to both always a right triangle?

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