#### Question

In the given figure, AB is the diameter of the circle with centre O.

If ∠ADC = 32°, find angle BOC

#### Solution

Arc AC subtends ∠AOC at the centre and ∠ADC at the remaining part Of the circle

∴ ∠AOC = 2 ∠ADC

⇒ ∠AOC = 2 × 32° = 64°

Since ∠AOC and ∠BOC are linear pair, we have

∠AOC + ∠BOC = 180°

⇒ 64° + BOC = 180°

⇒ ∠BOC = 180°

⇒ ∠BOC = 180° - 64°

⇒ ∠BOC = 116°

Is there an error in this question or solution?

Solution In the Given Figure, Ab is the Diameter of the Circle with Centre O. If ∠Adc = 32°, Find Angle Boc Concept: Arc and Chord Properties - the Angle that an Arc of a Circle Subtends at the Center is Double that Which It Subtends at Any Point on the Remaining Part of the Circle.