Question

In the figure below O is the centre of the circle and AB is the diameter. C is the point on the circle.

(i) Compute ∠CAB

(ii) Draw another figure like this with a different number for the size of ∠COB.

Calculate ∠CAB

Answer 1

(i) ∠BOC = 50°

∴ ∠COA = 180° – 50°= 130° (straight angle) OA = OC (radii)

∴ AOC is an isosceles triangle.

∴ ∠A = ∠C = \(\frac{180-130}{2}\) = 25°

(ii) ∠O = 70°

∴ ∠COA = 180 – 30 = 150°

OA = OC

∴ ∠CAB = ∠ACO = \(\frac{180-150}{2}=\frac{30}{2}\) = 15°