Chapter 9.7, Problem 16WE

To determine

To Find: Find the value of DP from the given figure.

Answer to Problem 16WE

The value of x is $\sqrt{10}$

Explanation of Solution

Given information: We have given $AP=6,BP=5,CP=3DP$ and a figure shown below

  

Let $DP=x$

As we know that when two chords intersect insides in a circle, then the product of the segments of one chord equals the product of the segments of the other chord.

Therefore, from given figure we must have

  $\begin{array}{c}AP\times PB=CP\times DP\\ 6\times 5=3x\times x\\ 30=3x^2\\ 10=x^2\\ x=\sqrt{10}\end{array}$

Therefore, the value of x is $\sqrt{10}$