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=(9\cdot72)/(14.4) \\ HY=45 \end{gathered}`

The length of HY is 45.