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1974 IMO Problems/Problem 2

Revision as of 16:38, 6 January 2019 by Speet (talk | contribs)

In the triangle ABC; prove that there is a point D on side AB such that CD is the geometric mean of AD and DB if and only if $\sin{A}\sin{B} \leq \sin^2 (\frac{C}{2})$.

Solution

Since this is an "if and only if" statement, we will prove it in two parts.

Part 1:

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