Two intersecting circles have a common chord of length 16 ft, and their centers lie on opposite sides of the chord. The radii of the circles are 10 ft and 17 ft respectively. Express the distance between the centers of the circles in feet.
Here's a pic :
The segment connecting their radii will bisect the chord at right angles
Using the PythagoreanTheorem, the distance between their centers will be given by :
DF + EF =
√[ 10^2 - 8^2] + √[17^2 - 8^2] =
√ [ 36] + √225 =
6 + 15 =
21 feet
