Question

In the figure, if O is the centre of the circle, then the measure of<ADC is
O​

Answer 1

The angle subtended by an arc is twice the angle subtended by it on the circumference in the alternate segment.

∠ADC=

2

1

∠AOC

=

2

1

×100

=50

∘

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Answer 2

Given:-

• Measure of ∠AOB is 62°.
• Measure of ∠BOC is 28°.

To find:-

• Measure of ∠ADC.

Solution:-

We know that,

Angle subtended by an arc at the center is double the angle subtended by it at any point on the remaining part of the circle.

So,

➝ ∠AOC = 2 ∠ADC

➝ ∠AOC/2 = ∠ADC

or, ∠ADC = ∠AOC/2 -----(i)

➝ ∠AOC = ∠AOB + ∠BOC

➝ 62° + 28°

➝ 90°

∠AOC = 90°

Now put ∠AOC in equation (i)

➝ ∠ADC = 90°/2

➝ ∠ADC = 45°

Therefore,

∠ADC is 45°.