Question

The diameter of a circle is 8 centimeters. a central angle of the circle of the circle intercepts an arc of 12 centimeters. what is the radian measure of the angle?

Answer 1

The diameter of the circle is 8 cm, so the radius of the circle is R=4cm.

The Circumference of the circle is 2πR=8π cm

Let the measure of the central angle be x.

the arc that angle x intercepts is 8/8π=1/π of the circumference. (approximately 1/3.14 or 1 third, so x will be 1 third of 360°=2π rad)

this is the ratio that x forms to the full angle 2π rad

$\frac{x}{2 \pi } = \frac{1}{ \pi }$

x= 2 rad.

Answer: 2 rad