Problem:
A circle has a chord of length 10 , and the distance from the center of the circle to the chord is 5 . What is the area of the circle?
Answer Choices:
A.
B.
C.
D.
E.
Solution:
Let the chord have endpoints and , and let be the center of the circle. The segment from to the midpoint of is perpendicular to and has length 5 . This creates the triangle , whose sides are 5,5 , and . Therefore the radius of the circle is , and the area of the circle is .
The problems on this page are the property of the MAA's American Mathematics Competitions