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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 $$\angle BPC.$$

285100_a44c5e6147254976887f15a7910d1a17.png


A
110
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B
140
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C
125
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D
136
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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

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