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Area of a Sector of a Circle

In the given ...

Question

In the given figure, AB and CD are diameters of a circle with centre O. If ∠OBD = 50°, find ∠AOC.

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Solution

It is given that, AB and CD are diameter with center O and

We have to find

Construction: Join the point A and D to form line AD

Clearly arc AD subtends at B and at the centre.

Therefore, $∠ A O D = 2 ∠ A B D = 100 °$ …… (1)

Since CD is a straight line then

$∠ D O A + ∠ A O C = 180 ° (Linear pair)$

Hence

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Similar questions

Q. In figure, AB and CD are diameters of a circle with centre O. If ∠OBD = 50⁰, find ∠AOC.

In the figure, AB and CD are diameters of a circle with centre O. If $∠ O B D = 50^{\circ}$ , find $∠ A O C$ .

Q. In the given figure, AB and CD are straight lines through the centre O of a circle. If ∠AOC = 80° and ∠CDE = 40°, find (i) ∠DCE, (ii) ∠OBC.

Q. In the figure given below,

A B

C D

are straight lines through the centre

O

of a circle. If

∠ A O C = 80^{o}

∠ C D E = 40^{o}

∠ D C E

∠ A B C

Q. In the given figure, BOC is a diameter of a circle with centre O. If AB and CD are two chords such that AB || CD. If AB = 10 cm, then CD = ?
(a) 5 cm
(b) 12.5 cm
(c) 15 cm
(d) 10 cm

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