Question

# In the given figure,$$AB$$ and $$AC$$ are tangents to the circle with centre $$O.$$Given that $$\angle BAC=70^{\circ}$$ and $$P$$ is a point on the minor arc $$BC,$$ find $$\angle BPC.$$

A
110
B
140
C
125
D
136

Solution

## The correct option is B $$125^{\circ}$$From the given figure,$$\angle COB+\angle CAB=180^{\circ}$$ (The angle between two tangents drawn from an external pt. to a circle is supplementary to the angle subtended by the line segments joining the points of contact at the centre)$$\Rightarrow$$ $$\angle COB=180^{\circ}-70^{\circ}=110^{\circ}$$Reflex $$\angle COB=360^{\circ}-110^{\circ}=250^{\circ}$$$$\therefore$$ $$\displaystyle \angle BPC=\frac{1}{2}\times$$ Reflex$$\displaystyle \angle AOB=\frac{1}{2}\times 250^{\circ} = 125^o$$(Angle subtended by the arc at the centre is twice the angle subtended at the circle)Mathematics

Suggest Corrections

0

Similar questions
View More

People also searched for
View More