1974 IMO Problems/Problem 2: Difference between revisions
Created page with "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 is less than or equal to sin²(C/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:
