Question

Q.90 In a circle with centre O, BC is a chord. Points D and A are on the circle, on the opposite side of BC, such that
DBC = 28º and BD = DC. What is the measure of BOC?
Ans

1. 98°
2. 84°
3. 112°
4. 96°​

Answer 1

Answer:

Step-by-step explanation:

112degree

Answer 2

Answer:

The Centre of the circle is O 

BC is a chord of the circle 

∠DBC = 28° and BD = DC

Concept used:

The complete angle is 360° 

In a triangle opposite angles of equal sides are equal.

The Sum of all internal angle in a triangle is 180° 

The angle subtended by an arc of a circle at its centre is twice the angle it subtends anywhere on the circle's circumference.

STEP BY STEP SOLUTION

Solution-.

∠DBC = ∠DCB = 28° 

In ΔDBC, 

∠DBC + ∠DCB + ∠BDC = 180° 

28° + 28° + ∠BDC = 180° 

56° + ∠BDC = 180° 

 ∠BDC = 180° – 56° 

 ∠BDC = 124° 

∠BOC = 2 × ∠BDC 

 ∠BOC = 2 × 124° 

∠BOC = 248° 

Complete angle at O = 360° 

248° + ∠BOC = 360° 

∠BOC = 112°