in figure 10.36 A, B and C are three points on a circle with Centre O such that angle BOC equal to 30 degree and Angle aob equal to 60 degree if D is a point on the circle and other than the earth ABC find angle ADC
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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°
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Hope this will help you....
∠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 this will help you....
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