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Question
A tangent PQ at a point P of a circle of radius 5 cm meets a line through the centre O at a point Q so that OQ = 12 cm. Length PQ is ______.
Options
12 cm
13 cm
8.5 cm
`sqrt119` cm
Solution
A tangent PQ at a point P of a circle of radius 5 cm meets a line through the centre O at a point Q so that OQ = 12 cm. Length PQ is `bbunderline(sqrt119 cm)`.
Explanation:
Suppose there is a circle whose center is O.
In right ΔQPO,
According to Pythagoras theorem,
OQ2 = OP2 + PQ2
= PQ = `sqrt(OQ^2 - OP^2)`
= PQ = `sqrt(12^2 - 5^2)`
= PQ = `sqrt(144 - 25`
= PQ = `sqrt119` cm.
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