Question

Find x. Assume that segments that appear tangent are tangent.
a.
56
c.
32
b.
28
d.
20

Answer 1

Answer:

c. 32

Step-by-step 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:

$x=\sqrt{40^2-24^2} \\ \\ x=\sqrt{1600-576} \\ \\ \boxed{x=32}$