Difference between revisions of "2002 AMC 12A Problems/Problem 22"
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Revision as of 15:25, 14 December 2010
Problem
Triangle is a right triangle with as its right angle, , and . Let be randomly chosen inside , and extend to meet at . What is the probability that ?
Solution
Clearly and . Choose a and get a corresponding such that and . For we need . Thus the point may only lie in the triangle . The probability of it doing so is the ratio of areas of to , or equivalently, the ratio of to because the triangles have identical altitudes when taking and as bases. This ratio is equal to . Thus the answer is .
See Also
2002 AMC 12A (Problems • Answer Key • Resources) | |
Preceded by Problem 22 |
Followed by Last Problem |
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 | |
All AMC 12 Problems and Solutions |