## Saturday, March 7, 2015

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## Saturday, March 7, 2015

Online Geometry theorems, problems, solutions, and related topics.

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Denote the 3 Cirles are (A; a), (C; c), (B; b) in the order given.

ReplyDeleteProjection A'B' of AB on the tangent line is sqrt[(a+b)^2 -(a-b)^2] = 2sqrt(ab)

Similar expressions for Proj's A'C', B'C' of AC, BC on the tangent line.

Clearly A'B' = A'C' +B'C' implies

2sqrt(ab) = 2sqrt(ac) + 2sqrt(bc)

Divide thro'out by 2sqrt(abc) to get the required result.