Question

If AC=12, BC=3, find CE

Answer 1

The correct answer is: 6

Answer 2

6

Explanation:

When you draw two secants to a circle from one exterior point as indicated in the Figure below, then the product of the external segment and the total length of each secant are equal, in other words:

`\overline{AB}. \overline{AD}=\overline{AC}. \overline{AE}`

Since in this problem we have a tangent line, from the figure we have:

`\overline{AC}. \overline{BC}=\overline{CE}. \overline{CE} \\ \\ \overline{CE}^2=\overline{AC}. \overline{BC} \\ \\ \overline{CE}=\sqrt{\overline{AC}. \overline{BC}} \\ \\ \overline{CE}=√(12* 3)=√(36) \\ \\ \therefore \boxed{ \overline{CE}=6}`