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प्रश्न
If from an external point P of a circle with centre O, two tangents PQ and PR are drawn such that ∠QPR = 120°, prove that 2PQ = PO.
उत्तर
Let us draw the circle with external point P and two tangents PQ and PR.
We know that the radius is perpendicular to the tangent at the point of contact.
∴∠OQP=90°
We also know that the tangents drawn to a circle from an external point are equally inclined to the segment, joining the centre to that point.
∴∠QPO=60°
Now in ∆QPO:
`cos60^@="PQ"/"PO"`
`⇒1/2="PQ"/"PO"`
`⇒2PQ=PO`
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