1. In Fig. 10.36, A,B and C are three points on a
circle with centre O such that Z BOC = 30° and
Z AOB = 60°. If D is a point on the circle other
than the arc ABC, find ZADC.
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Answered by
20
∠AOB = 60°
∠BOC= 30°
∠AOC = ∠AOB + ∠BOC
∠AOC = 60°+30°
∠AOC = 90°
Arc ABC makes an angle of 90° at the centre of the circle.
∠ADC= 1/2∠AOC
[SINCE THE ANGLE SUBTENDED BY AN ARC AT THE CENTRE IS DOUBLE THE ANGLE SUBTENDED BY IT AT ANY POINT ON THE REMAINING PART OF THE CIRCLE]
∠ADC= 1/2(90°)
∠ADC= 45°
∠ADC= 45°
Answered by
8
Given:−
- ∠AOB = 60°
- ∠BOC= 30°
Here,
- ∠AOC = ∠AOB + ∠BOC
- ∠AOC = 60°+30°
- ∠AOC = 90°
Since,
- Arc ABC makes an angle of 90° at the centre of the circle.
∠ADC= 1/2∠AOC
- [SINCE THE ANGLE SUBTENDED BY AN ARC AT THE CENTRE IS DOUBLE THE ANGLE SUBTENDED BY IT AT ANY POINT ON THE REMAINING PART OF THE CIRCLE]
∠ADC= 1/2(90°)
∠ADC= 45°
Hence,
- ∠ADC= 45°
Hope it will be helpful :)
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