The weather balloon

A circle with three red tangents. The tangency points are marked red. Prove that the yellow triangle is isosceles.

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The horizontal line is the radical axis between the balloon and a zero-radius circle centered at the bottommost point of the diagram (the intersection of the two red tangents). Points on the radical axis have the same power to the circles, so the yellow triangle is isosceles.

Solution by Marshall W. Buck

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