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Collinear intersections (Posted on 2009-07-13) Difficulty: 2 of 5
Two smaller circles of radii a and b are internally tangent to a larger circle, of radius r, at points P and Q respectively. The smaller circles intersect at points S and T.

If P, S, and Q are collinear, prove that r = a+b.

See The Solution Submitted by Bractals    
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re: proof | Comment 2 of 3 |
(In reply to proof by Charlie)

Don't you also have to show that BS is parallel to PAR before you can say that ASBR is a parallelogram?

Clearly, the argument is similar to showing AS is parallel to QBR.

  Posted by Bractals on 2009-07-14 01:16:25
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