Question

Find x. Assume that segments that appear tangent are tangent.

a.
56
c.
32
b.
28
d.
20

Answer 1

c. 32

Explanation:

The problem states that we need to assume that segments that appear tangent are actually tangent. From the figure, the tangent segment is the one that measures
`x` while the radius measures 24. The key in this problem is that if a radius of a circle and a tangent line to that circle touch intersect at the same point, then they form a right angle there. Accordingly, we have a right triangle here, so using the Pythagorean theorem, we can find
`x`. Thus:

`x=√(40^2-24^2) \\ \\ x=√(1600-576) \\ \\ \boxed{x=32}`