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

The length of the intercepted arc can be calculated through the equation,

A = (θ/2π) (2πr)

where r is the radius. We are given that the value of diameter is 8 cm. Radius can be calculated by dividing the given diameter by 2.

radius = 8 cm/2 = 4 cm

Substituting the known values to the equation above,

12 cm = (θ/2π) (2π) (4 cm)

The value of θ from the equation is 3.

Answer: 3 radians