Chapter 9.7, Problem 11WE

To determine

To prove: $UV\cdot UW=UX\cdot UY$

Explanation of Solution

Given information:

Given figure,

$\odot O$ and $\odot P$ are tangent to $\overline{UT}$ at $T$ .

Calculation:

When a secant segment and a tangent segment are drawn to a circle from an external point, the product of the secant segment and its external segment is equal to the square of the tangent segment.

For point $O$ ,

For point $P$ ,

  $UX\cdot UY=U{T}^2$

Therefore, it is proved that $UV\cdot UW=UX\cdot UY$ .