Q14. - Geometry

Question

For each exercise draw $\odot O$ with radius $12$. Then draw radii $\overline{OA}$ and to $\overline{OB}$ form an angle with the measure named. Find the length of $\overline{AB}$.

 c. $m\angle AOB=60°$

Step-by-Step Solution

Answer

$AB=12$.

Step 1. Given information.

Step 2. Concept used.

Equilateral triangle concept. 

Step 3. Find value.

Since, from the figure:

$AO=OB=12$

Then, $\angle A=\angle B$

Now,  

$\begin{array}{c}\angle A+\angle B+\angle O={180}^{\circ }\\ 2\angle A+{60}^{\circ }={180}^{\circ }\\ \angle A={60}^{\circ }\\ \angle B={60}^{\circ }\end{array}$

$\Delta ABC$is a equilateral triangle.

So, all sides are equal:

$AO=OB=AB$

Therefore, $AB=12$