Question

In the fig. A, B and C are three points on a circle with centre O such that BOC = 30° and AOB = 60. If D is a point on the circle other than the arc ABC, find ADC.
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Answer 1

Answer:

The <ADC = 45°

Step-by-step explanation:

As we can see that

<AOC = <AOB + < BOC

=> 60° = <AOB + 30°

Now,

<AOC = 2x <ADC [ The subtended of an arc at the centre is double the angle subtended by it at point of the circle]

<ADC = 1/2 <AOC = 1/2×90°

=> 45°

Hence,<ADC is 45°.

Answer 2

$\huge \underline \mathbb {SOLUTION:-}$

∠ AOC = ∠ AOB + ∠ BOC

➠ 60° + 30°

➠ 90°

Arc ABC subtends ∠ AOC at center of circle.

And, ∠ ADC on point D

Therefore:

∠ AOC = 2 ∠ ADC

• Angle subtended by arc at the center is double the angle subtended by it at any other point.

90° = 2 ∠ ADC

2 ∠ ADC = 90°

∠ ADC = 1/2 × 90°

∠ ADC = 45°

• Hence, the ∠ ADC = 45°

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