# In the diagram below, if OM=8 and MY=9, what does XZ equal?

Jun 8, 2018

The answer is d.
$X Z = 30$

#### Explanation:

From the problem: $O M = 8$ and $M Y = 9$

The radius of the circle can be obtained by:
$O Y = O M + M Y = 8 + 9 = 17$

But $O X$ is also the radius, so:
$O X = O Y = 17$

In the right triangle $\triangle O X M$, we can apply Pythagoras:
$O {X}^{2} = O {M}^{2} + X {M}^{2}$

${17}^{2} = {8}^{2} + X {M}^{2}$
$X {M}^{2} = 289 - 64 = 225$

So, $X M = 15$

Since $X Z = 2 \cdot X M$

then: $X Z = 30$