Mathematics
In the given figure, AOB is a diameter of the circle with centre O and ∠AOC = 100°, find ∠BDC.
Circles
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Answer
From figure,
∠AOC + ∠BOC = 180° [Linear pair]
100° + ∠BOC = 180°
∠BOC = 180° - 100°
∠BOC = 80°.
We know that,
Angle which an arc subtends at the centre is double that which it subtends at any point on the remaining part of the circumference.
⇒ ∠BOC = 2∠BDC
⇒ 80° = 2∠BDC
⇒ ∠BDC = = 40°
Hence, ∠BDC = 40°.
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