Question

Question 3.
(a) In the following figure, angle AOB = 130° where O is the centre of the circle. Find angle BCO and angle BDC.​

Answer 1

Answer:

BCO = 65⁰

BDC = 25⁰

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Answer 2

As Arc $AB$ subtends $130 \degree$ at the centre, then it must subtend half the angle on the circle.

$\angle BCO = \dfrac{1}{2} ( \angle AOB) \\ \\ \angle BCO = \dfrac{1}{2} (130 \degree) \\ \\ \angle BCO = 65 \degree$

Similarly, Angle made by Arc $BC$ on the centre is $180 \degree - 130 \degree = 50 \degree$, then it must subtend half the angle on the center.

$\angle BDC = \dfrac{1}{2} ( \angle BOC) \\ \\ \angle BDC = \dfrac{1}{2} (50 \degree) \\ \\ \angle BDC = 25 \degree$

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