C3: Angles in Circles

A circle has a central angle of 210°. 
The arc length of that angle is 7 $\pi$ inches.
Find the radius of the circle. 

The intercepted arc length in a circle is 16π. If the radian measure of the arc is  $\frac{2}{3}\pi$ radians  , what is the radius of the circle?

Find the length of an arc in a circle with a radius of 4 in, and a central angle of  $\frac{4}{3}\pi$    radians.

•  $\frac{1}{3}\pi$  

•  $\frac{16}{3}\pi\$  

•  $\frac{32}{3}\pi$  

•  $\frac{4}{135}\pi^2$  

Find the radian measure of a central angle that measures 40°.

• Cannot be found without a radius length.

• $\frac{9}{2\pi}$

• $\frac{7200}{\pi}$

• $\frac{2}{9}\pi$

The wheels of Sahil’s bike each have a 10-in. diameter. Katie’s mountain bike has wheels with a 12-in. diameter. How much farther does Katie’s bike travel after 5 revolutions than Sahil’s bike?

• 10 inches

• $55\pi^2$ inches

• $2\pi$ inches
  

• $10\pi$ inches

Write the equation of a circle that centers on (4, -3) and has a radius of 5.

• $\left(x-4\right)^2+\left(y+3\right)^2=25$

• $\left(x+4\right)^2+\left(y-3\right)^2=25$

• $\left(x-4\right)^2+\left(y+3\right)^2=5$

• $x^2+y^2=5$

Find the value of angle a. Angles a, b, and c are not congruent.

Find the measure of angle b. Angles a, b, and c are not congruent.

Find the measure of angle c. Angles a, b, and c are not congruent.

Find the measure of angle b.