Question

In the figure below, AB and CD are arcs of two concentric circles, centre O. Angle AOB = 60° and AD=BC=7cm.

Given that the perimeter of ABCD is 28 ²/₃ cm, find OA, the radius of the inner circle. 

Answer 1

θ=60°=π/3radians
Arc length =θr where θ is in radians
^π/₃ × r + ^π/₃×(r+7) +7+7 =28 ²/₃
^2π/_3r =14 ²/₃− ^7π/₃
        r=3.502