Question

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.​

Answer 1

${\huge{\underline{\small{\bold{\red{Answer:-}}}}}}$

${\huge{\underline{\small{\bold{\orange{Given:-}}}}}}$

$⇝$∠AOB = 60°

$⇝$∠BOC= 30°

${\huge{\underline{\small{\bold{\pink{Here,}}}}}}$

$⇝$∠AOC = ∠AOB + ∠BOC

$⇝$∠AOC = 60°+30°

$⇝$∠AOC = 90°

${\huge{\underline{\small{\bold{\orange{Since,}}}}}}$

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°

${\huge{\underline{\small{\bold{\blue{Hence,}}}}}}$

$⇝$ ∠ADC= 45°

${\huge{\underline{\sf{\bold{\red{Hope\:help\:u:)}}}}}}$

Answer 2

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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°

Hope it will be helpful :)