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प्रश्न
The length of the tangent from an external point P to a circle of radius 5 cm is 10 cm. The distance of the point from the centre of the circle is ______.
पर्याय
8 cm
`sqrt(104)` cm
12 cm
`sqrt(125)` cm
MCQ
रिकाम्या जागा भरा
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उत्तर
The length of the tangent from an external point P to a circle of radius 5 cm is 10 cm. The distance of the point from the centre of the circle is `underlinebb(sqrt(125) cm)`.
Explanation:
If O is the centre and PT is the tangent (length 10) meeting the circle at T, then OT = radius = 5 and OT ⟂ PT, so triangle OTP is right.
By Pythagoras, `OP = sqrt(OT^2 + PT^2)`
= `sqrt(5^2 + 10^2)`
= `sqrt(125)`
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