Question

A circle is shown belowIf FM=11, MG=3, and PM=2, What is the measure of PQ?A. 16.5B. 18.5C. 7.3D.9.3

Answer 1

To solve this question we need to remember the thales theorem, then:

$\frac{PQ}{PM}=\frac{GF}{MG}$

But we can see from the image that GF= MG+FM, then

$\frac{PQ}{PM}=\frac{MG+FM}{MG}$

then we can replace the known numbers in the previous expression:

$\frac{PQ}{2}=\frac{3+11}{3}$$PQ=\frac{2(14)}{3}=\frac{28}{3}=9.3$