Question

in the figure below, two seconds are drawn to a circle from exterior point H. Suppose that HW=72, HZ=9, and HX=14.4. Find HY.

Answer 1

When two secants are arranged in the form of the picture the segments must obey the following rule:

$HX\cdot HY=HZ\cdot HW$

Applying the data from the problem we have:

$\begin{gathered} 14.4\cdot HY=9\cdot72 \\ HY=\frac{9\cdot72}{14.4} \\ HY=45 \end{gathered}$

The length of HY is 45.