1958 AHSME Problems/Problem 48
Problem
Diameter of a circle with center is units. is a point units from , and on . is a point units from , and on . is any point on the circle. Then the broken-line path from to to :
Solution
- If somebody wants to draw a diagram or make this solution better, PLEASE do so. I cannot express how bad I am at this.
If P is on A, then the length is 10, eliminating answer choice (B). If P is equidistant from C and D, the length is 2=2>10, eliminating (A) and (C). If CDP is a right triangle, then CDP will be right or DCP will be right. Assume that DCP is right. Then, APB is right, so CP==. Then, DP=, so the length we are looking for is +>10, eliminating (D). Thus, our answer is (E).
See Also
1958 AHSC (Problems • Answer Key • Resources) | ||
Preceded by Problem 47 |
Followed by Problem 49 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 • 26 • 27 • 28 • 29 • 30 • 31 • 32 • 33 • 34 • 35 • 36 • 37 • 38 • 39 • 40 • 41 • 42 • 43 • 44 • 45 • 46 • 47 • 48 • 49 • 50 | ||
All AHSME Problems and Solutions |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.