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# In the Given Figure, Ab is the Diameter of the Circle with Centre O. If ∠Adc = 32°, Find Angle Boc - ICSE Class 10 - Mathematics

ConceptArc 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

#### 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 × 32° = 64°
Since ∠AOC and ∠BOC are linear pair, we have
∠AOC + ∠BOC = 180°
⇒ 64° + BOC = 180°
⇒ ∠BOC = 180°
⇒ ∠BOC = 180° - 64°
⇒ ∠BOC = 116°

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#### Video TutorialsVIEW ALL [1]

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.
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