1953 AHSME Problems/Problem 14
Problem 14
Given the larger of two circles with center and radius and the smaller with center and radius . Draw . Which of the following statements is false?
Solution
We will test each option to see if it can be true or not. Links to diagrams are provided. Let circle be inside circle and tangent to circle , and the point of tangency be . , and , so Let circle be outside circle and tangent to circle , and the point of tangency be . , and , so Let circle be outside circle and not tangent to circle , and the intersection of with the circles be and respectively. and , and , so Let circle be inside circle and not tangent to circle , and the intersection of with the circles be and as shown in the diagram. and , and , so , and , so Since options A, B, C, and D can be true, the answer must be .
See Also
1953 AHSC (Problems • Answer Key • Resources) | ||
Preceded by Problem 13 |
Followed by Problem 15 | |
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.