Segment AD is perpendicular to the radius of circle (B) and the radius of circle (c). If radius BA=6in, segment AD=21in and radius CD=16in, find the length of BC to the nearest tenth of an inch.

Answer 1

Let M be the midpoint of AD.
Then you have two right triangles BMA and DMC where you know the hypotenuse and one leg.

Use the Pythagorean Theorem to find BM and MC.

Answer 2

Find the segment that makes BC the hypotenuse of a right triangle by finding a segment with an endpoint B that is perpendicular to CD. You can do this by subtracting DC and BA to get a segment with the length of 10. This segment is parallel to AD so you know that the length will also be 21. Use Pythagorean Theorem with the values 10 and 21 to find the hypotenuse BC.

10^2 + 21^2 = (BC)^2
100 + 441 = (BC)^2
541 = (BC)^2
square root of 541 = BC
BC is about 23.3 inches