In this figure points A B and C are on the circle with the c

In this figure, points A, B and C are on the circle with the center point O. Point D is the intersection of the radius OB and chord AC, the angle AOD = 110 degree and angle BDC = 50 degree. Determine the angle (angle CBD).

Solution

Angle subtented at center is twice the angle subtended by a point on circle

So BCA = 110/2 = 55

In triangle BCD, we have:

CBD + BCD + BDC = 180
55+50+CBD = 180
CBD = 75

S0, answer is 75