Chapter 10.8, Problem 17PSC

To determine

find DE and DC.

Answer to Problem 17PSC

  $DE=26,DC=39$

Explanation of Solution

Given information:

Given concentric circles as shown,

  

Calculation:

Consider the figure,

  

  $\begin{array}{l}BC=3\\ EF=4\end{array}$

Apply Secant-secant power theorem on inner circle,

  $\begin{array}{l}3x=2y\\ y=1.5x\mathrm{...}\left(1\right)\end{array}$

Apply Secant-secant power theorem on outer circle,

  $\begin{array}{l}\left(4+3\right)\left(x+EF\right)=\left(3+2\right)\left(y+BC\right)\\ 7\left(x+4\right)=5\left(y+3\right)\\ 7x+28=5y+15\\ 7x-5y=-\mathrm{13.....}\left(2\right)\end{array}$

  $\begin{array}{l}puty=1.5xine{q}^n\left(2\right)weget,\\ 7x-5y=-13\\ 7x-5\left(1.5x\right)=-13\\ 7x-7.5x=-13\\ -.5x=-13\\ x=26\\ y=1.5\left(26\right)\\ y=39\end{array}$

Hence, $DE=26,DC=39$ .