1997 AHSME Problems/Problem 19
Contents
Problem
A circle with center is tangent to the coordinate axes and to the hypotenuse of the -- triangle as shown, where . To the nearest hundredth, what is the radius of the circle?
Solution
Draw radii and to the axes, and label the point of tangency to triangle point . Let the radius of the circle be . Square has side length .
Because and are tangents from a common point , .
Similarly, , and we can write:
Equating the radii lengths, we have
This means
by the 30-60-90 triangle.
Therefore, , and we get
The radius of the circle is , which is
Using decimal approximations, , and the answer is .
Solution 2
From the diagram above, it is more direct to note that BC = CF + BF = r - + r - 1 = 2
See also
1997 AHSME (Problems • Answer Key • Resources) | ||
Preceded by Problem 18 |
Followed by Problem 20 | |
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