Question

The radii of two concentric circles are $15$cm and $7$cm. A diameter $\overline{AB}$of the larger circle intersects the smaller circle at $C$and $D$. Find two possible values for $AC$.

Short answer

$8cm$ or $22cm$.

Step-by-step solution

Step 1. Given information. 

The radii of two concentric circles are $15$cm and $7$cm. A diameter $\overline{AB}$of the larger circle intersects the smaller circle at $C$ and $D$.

Step 2. Concept used.

Concentric circles are circles with a common center.

Step 3. Find possible values.

From the figure, two possible values of $AC$are:

$\begin{array}{l}AC=AO-OC\\ AC=15-7\\ AC=8cm\end{array}$

Or

$\begin{array}{l}AC=AO+OC\\ AC=15+7\\ AC=22cm\end{array}$

Therefore, possible values are $8cm$ or $22cm$.