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Four Circles (Posted on 2008-04-24) Difficulty: 3 of 5


Let P(r) denote the circle with point P as its center and r as its radius.

Let AB be a chord of O(r) and let the perpendicular bisector of AB intersect O(r)
at points C and D and chord AB at point M such that M lies between O and C.

Let O1(r1), O2(r2), and O3(r3) lie within circular segment ADB and be tangent to AB.

Let O1(r1) and O3(r3) be internally tangent to O(r) and externally tangent to O2(r2), but not intersect each other.

If r2 = |MC|/2, then prove that r = r1 + r2 + r3

See The Solution Submitted by Bractals    
Rating: 2.0000 (1 votes)

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