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

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Answer 1 · 2018-06-08T05:19:20

The answer is d.
$X Z = 30$ $XZ = 30$

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

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

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

In the right triangle $△ O X M$ $triangleOXM$ , we can apply Pythagoras:
$O X^{2} = O M^{2} + X M^{2}$ $OX^2 = OM^2+XM^2$

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

So, $X M = 15$ $XM=15$

Since $X Z = 2 \cdot X M$ $XZ = 2*XM$

then: $X Z = 30$ $XZ = 30$