Question

Two circle with different radius intersect each other in such a way that the centre of smaller circle falls on the circumference of the bigger circle. If angleADC=74 degree ; find the value of angleAOC.

Answer 1

see diagram.

∠ADC = 74°
∠ADO = 74°/2 = 37°

In the Isosceles triangle ΔDAO,  DA = DO = Radius
         ∠DOA = (180° - ∠ADO)/2 = 143°/2
ΔDCO is congruent to ΔDAO as the common chord and perpendicular to DO and it is symmetric about DO.

  So ∠AOC = 2 * 143°/2  = 143°