1979 AHSME Problems/Problem 17
Problem 17
Points , and are distinct and lie, in the given order, on a straight line. Line segments , and have lengths , and , respectively. If line segments and may be rotated about points and , respectively, so that points and coincide, to form a triangle with positive area, then which of the following three inequalities must be satisfied?
Solution
Solution by e_power_pi_times_i
We know that this triangle has lengths of , , and . Using the Triangle Inequality, we get inequalities: . Therefore, we know that is true and is false. In , we have to prove . We know that , so we have to prove . , so we have to prove that , which is true for all positive . Therefore the answer is .
See also
1979 AHSME (Problems • Answer Key • Resources) | ||
Preceded by Problem 16 |
Followed by Problem 18 | |
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