Chapter 9, Problem 10CT

To determine

To calculate: $OE$

Answer to Problem 10CT

  $OE=8$

Explanation of Solution

Given information: Radius of circle is $17$ and $AB=30$

Calculation:

  

Join OA and OB.

  $OE\perp AB$

As perpendicular from the center to the chord bisects the chord,

  $AE=\frac{1}{2}AB$

Put $AB=30$

So,

  $AE=\frac{1}{2}\left(30\right)=15$

Also, radius of circle is equal to 17.

So,

  $AO=17$

In a right-angled triangle, square of hypotenuse is equal to the sum of squares of other two sides.

  $\begin{array}{l}A{O}^2=O{E}^2+A{E}^2\\ \Rightarrow {17}^2=O{E}^2+{15}^2\\ \Rightarrow 289=O{E}^2+225\\ \Rightarrow O{E}^2=289-225=64\\ \Rightarrow OE=\sqrt{64}=8\end{array}$