In figure below, O is the center of the circle and A, B are point on the circle.

Question

In figure below, O is the center of the circle and A, B are point on the circle. Compute ∠ A and ∠ B.

Philoid · Accepted Answer

In Δ OAB,

OA = OB = r = Radius of circle

In a triangle with 2 equal sides, the angles opposite to equal sides are equal.

∴ ∠OAB(∠A) = ∠OBA(∠B) = y° …(eq)1

In a triangle,

Sum of all angles of a triangle is 180°

∴ In Δ OAB,

∠O + ∠A + ∠B = 180°

∴ 60 + y + y = 180°

∴ 60 + 2y = 180°

∴ 2y = 180-60

= 120

∴

∴ ∠A = ∠B = 60° (from eq1)