Circle a and circle b are congruent. cd is a chord of both circles. if ab = 8 ft and cd = 6 ft, how long is a radius? 6 ft 5 ft 7 ft 8 ft

Since circle A and circle B are congruent, then therefore they have similar radius. Let us say that the intersection of segments AB and CD is called point E. The two segments are perpendicular to each other therefore forming a 90 degrees angle at each corner.

To solve this problem, we draw an imaginary line connecting points C and B, thus creating triangle CEB which is a right triangle. We now see that line CB is the hypotenuse of the triangle and at the same time the radius of the circle.

We are given that:

CD = 6 ft               therefore            CE = 3 ft

AB = 8 ft               therefore            EB = 4 ft

Hence using the Pythagorean Theorem:

CB^2 = CE^2 + EB^2

CB^2 = 3^2 + 4^2

CB^2 = 9 + 16

CB^2 = 25

CB = 5 ft