Difference between revisions of "1974 IMO Problems/Problem 2"
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In the triangle ABC; prove that there is a point D on side AB such that CD | 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 | + | is the geometric mean of AD and DB if and only if |
| + | <math>\sin{A}\sin{B} \leq \sin^2 (\frac{C}{2})</math>. | ||
| − | + | ==Solution== | |
| + | |||
| + | Since this is an "if and only if" statement, we will prove it in two parts. | ||
| + | |||
| + | Part 1: | ||
Revision as of 16:38, 6 January 2019
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
.
Solution
Since this is an "if and only if" statement, we will prove it in two parts.
Part 1:
