Question

A circle with radius r and centre o. The points A, , C on the circle and AOC = theta. The area of sectoer OABC is 4/3π and the length of arc ABC is 2/3π What is the value of r and theta?

Answer 1

\[ Area = \pi (r^2) \frac{\theta}{360}\]\[ \frac{4\pi}{3} = \pi (r^2) \frac{\theta}{360}\]\[ 480 = r^2 \theta \ -(1)\]
Arc length = 2pi r (theta /360)
(2/3 ) pi = 2 pi r (theta /360)
120 = r theta -(2)
Solve the 2 equations.

Answer 2

Try (1) / (2), that would be a fast way to solve the equations. You'll get r from that.