Difference between revisions of "1991 AHSME Problems/Problem 23"
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Revision as of 13:25, 14 December 2016
Problem
If is a square, is the midpoint of , is the midpoint of , and intersect at , and and intersect at , then the area of quadrilateral is
Solution 1: Coordinate Geometry
Solution by e_power_pi_times_i
First, we find out the coordinates of the vertices of quadrilateral , then use the Shoelace Theorem to solve for the area. Denote as . Then . Since I is the intersection between lines and , and since the equations of those lines are and , . Using the same method, the equation of line is , so . Using the Shoelace Theorem, the area of is .
See also
1991 AHSME (Problems • Answer Key • Resources) | ||
Preceded by Problem 22 |
Followed by Problem 24 | |
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 | ||
All AHSME Problems and Solutions |
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