Question

In Fig. 16.182, AB and CD are diameters of a circle with centre O. If ∠OBD=50°, find ∠AOC.

Answer 1

Answer:

OB = OD ( RADIUS)

OB = 50° ( ISOSCELES TRIANGLE PROPERTY)

IN TRIANGLE ODB

D + O+ B = 50 +50+O=180 (ASP)

O = 80

ANGLE AOC IS VERTICALLY OPPOSITE ANGLE THEREFORE ANGLE AOC IS 80°

HENCE, THE ANSWER IS 80°

HOPE IT HELPS YOU.....

Answer 2

The value of $\angle AOC$ is 80°

Explanation:

It is given that AB and CD are diameters of a circle with centre O.

Also, given that $\angle \mathrm{OBD}=50^{\circ}$

We need to determine $\angle \mathrm{AOC}$

First, we shall construct a line joining the points A and D to form a line AD.

Thus, from the figure, it is obvious that $\angle A B D=50^{\circ}$ and $\angle A O D$ at the centre.

Thus, we have,

$\angle A O D=2 \angle A B D$

           $=2(50)$

$\angle A O D=100^{\circ}$

Since, we can see that CD is a straight line and the angles in a straight line add upto 180°

Thus, we have,

$\angle D O A+\angle A O C=180^{\circ}$

   $100^{\circ}+\angle A O C=180^{\circ}$

              $\angle A O C=80^{\circ}$

Thus, the value of $\angle AOC$ is 80°

Learn more:

(1) In the given figure AB and CD are diameters of a circle with centre O.If angle OBD=40° find angle AOC and angle ACD

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(2) In the figure , O is the centre of the circle. Find angle CBD

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