1970 AHSME Problems/Problem 7
Problem
Inside square with side , quarter-circle arcs with radii and centers at and are drawn. These arcs intersect at a point inside the square. How far is from the side of ?
Solution
All answers are proportional to , so for ease, let .
Let be oriented so that .
The circle centered at with radius is . The circle centered at with radius is . Solving each equation for to find the intersection leads to , which leads to .
Plugging that back in to leads to , or . Since we want the intersection within the square where , we take the positive solution, and the intersection is at $X(\frac{1}{2}, \frac{\sqrt{3}}{2}}$ (Error compiling LaTeX. ! Extra }, or forgotten $.).
The distance from to side , which lies along the line , is , or . This is answer when .
See also
1970 AHSC (Problems • Answer Key • Resources) | ||
Preceded by Problem 6 |
Followed by Problem 8 | |
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