Question

# In the given figure, O is the centre of the circle. A is any point on minor arc BC. Find the value of ∠BAC−∠OBC.

A

90

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
B

120

No worries! We‘ve got your back. Try BYJU‘S free classes today!
C

60

No worries! We‘ve got your back. Try BYJU‘S free classes today!
D

45

No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

## The correct option is A 90∘ Here OB = OC = radius ⇒ΔOBC is isosceles ∴∠OBC=∠OCB=y∘ Now in ΔOBC, by angle sum property ∠OBC+∠OCB+∠BOC=180∘ y+y+t=180∘ 2y+t=180∘ 2y+(360∘−∠z)=180∘ [∠z is the reflex ∠ of ∠t] 2y+360∘−∠z=180∘ Reflex ∠z=2x [Angle subtended by an arc at the centre is twice the angle subtented by it at the circumference] ⇒2y+360∘−2x=180∘⇒2y−2x=180∘−360∘⇒2y−2x=−180∘⇒y−x=−90∘⇒x−y=90∘ Thus ∠BAC−∠OBC=90∘

Suggest Corrections
5
Join BYJU'S Learning Program
Select...
Related Videos
Circles and Quadrilaterals - Theorem 8
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
Select...