Question #N290
A circle with center O has radius 5. A chord AB of the circle is 8 units long. What is the distance, in units, between the midpoint of AB and point O?
A. 1
B. 3
C. 4
D. 5
Correct Answer is: B
Draw a radius from O to the midpoint of AB. This radius bisects chord AB, forming two right triangles. The hypotenuse of each triangle is 5, and one leg is 4. The Pythagorean theorem states that 5^2 = 4^2 + x^2, where x is the distance between the midpoint of AB and point O. Solving, we find x^2 = 9, so x = 3. Therefore, the distance between the midpoint of AB and point O is 3.