Question

In the given figure, AB is a diameter of the circle with centre O. If ∠BOC = 110°, find ∠ADC.

Answer 1

AB is a diameter, so central angle.

∠AOB = 180°

Point C lies on arc AB, and we are given

∠BOC = 110°

∠AOC = 180° − 110° = 70°

So arc AC measures 70°.

Angle ∠ADC is an inscribed angle subtending arc AC

∴ ∠ADC = `1/2 xx  "arc" AC = 1/2 xx` 70° = 35°

∠ADC = 35°