EXERCISE 10.5301. In Fig. 10.36, A,B and C are three points on acircle

1.	EXERCISE 10.5301. In Fig. 10.36, A,B and C are three points on acircle with centre O such that BOC 30° andL AOB 600. If D is a point on the circle other0.than the arc ABC, find ZADC.Fig. 10.36
Answer» ∠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°

EXERCISE 10.5301. In Fig. 10.36, A,B and C are three points on acircle with centre O such that BOC 30° andL AOB 600. If D is a point on the circle other0.than the arc ABC, find ZADC.Fig. 10.36

Answer»

∠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°