Chapter 9.7, Problem 20WE

To determine

The value of PT and PC from the given figure

Answer to Problem 20WE

The value of PT= $\sqrt{50}$ and PC = 12.5

Explanation of Solution

Given information:

It is given PB = 5, PD = 4, AB = 5 and a figure,

  

Let PT = x

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

Therefore, from the given figure

  $\begin{array}{c}P{T}^2=PB\times PA\\ x^2=5\times \left(5+5\right)\\ x^2=5\times 10\\ x=\sqrt{50}\end{array}$

Since length is positive so we neglect the negative value so PT= $\sqrt{50}$

Also

  $\begin{array}{c}P{T}^2=PD\times PC\\ {\left(\sqrt{50}\right)}^2=4\times PC\\ PC=\frac{50}{4}\\ PC=12.5\end{array}$

Therefore the value of PC = 12.5