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In the given figure, two tangents RQ and...

In the given figure, two tangents `RQ` and `RP` are drwn from an external point `R` to the circle with centre `O`. If `/_PRQ=120^(@)`, then prove that ``OR=PR+RQ`.

Text Solution

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Join `OP` and `OQ`.
`/_PRQ=120^(@)implies/_PRO=/_QRO=(1)/(2)xx/_PRQ=60^(@)`. [`:'` two tangents from an external point are equally inclined to the line segement joining the centre to that point. And so, `/_PRO= /_QRO=(1)/(2)/_PRQ`.
In right `DeltaOPR`, we have
`cos=/_PRO=(PR)/(OR)impliescos60^(@)=(PR)/(OR)implies(1)/(2)=(PR)/(OR)impliesPR=(1)/(2)xxOR`.
Similarly, `RQ=(1)/(2)xxOR`.
`:.PR+RQ=OR`.
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