In the given figure , 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?

# In the given figure , 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?

1. A
45$°$
2. B
90$°$
3. C
120$°$
4. D
180$°$

Fill Out the Form for Expert Academic Guidance!l

+91

Live ClassesBooksTest SeriesSelf Learning

Verify OTP Code (required)

### Solution:

∠BOC=30$°$ and ∠AOB=60$°$ (Given)
⇒∠AOC= ∠AOB + ∠BOC
⇒∠AOC= 60$°$+30$°$
⇒∠AOC= 90$°$
We can see that AOC is the angle subtended by the arc ABC at its centre.
D is now the point on the circle that is not the arc ABC.
As a result, we know that the angle subtended by an arc at the centre is twice that of any other point on the circle.
Therefore,
⇒ 90$°$ = 2×∠ADC
$⇒\frac{90°}{2}=\angle \mathit{ADC}$
⇒ 45$°$= ∠ADC
Hence we get the value of ∠ADC as 45$°$.

## Related content

 Area of Square Area of Isosceles Triangle Pythagoras Theorem Triangle Formula Perimeter of Triangle Formula Area Formulae Volume of Cone Formula Matrices and Determinants_mathematics Critical Points Solved Examples Type of relations_mathematics

+91

Live ClassesBooksTest SeriesSelf Learning

Verify OTP Code (required)