FidgetBoss 4000's 2019 Mock AMC 12B Problems/Problem 2
Problem
(fidgetboss_4000) In the diagram below, is an isosceles right triangle with a right angle at and with a hypotenuse of units. Find the greatest integer less than or equal to the value of the radius of the quarter circle inscribed inside .
Solution
The quarter circle is centered at and just touches the hypotenuse at the midpoint of the hypotenuse due to symmetry in an isosceles right triangle. The value of its radius is equal to the distance between and the midpoint of the hypotenuse, and it is well known that this is half the length of the hypotenuse, or . The greatest integer less than or equal to is , thus we pick answer .
See also
FidgetBoss 4000's 2019 Mock AMC 12B (Problems • Answer Key • Resources) | |
Preceded by Problem 1 |
Followed by Problem 3 |
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All AMC 12 Problems and Solutions |
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