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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 such that OQ = 12 cm. Length PQ is
  • a)
    12 cm
  • b)
    13 cm
  • c)
    8.5 cm
  • d)
    √119 cm
Correct answer is option 'D'. Can you explain this answer?
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A tangent PQ at a point P of a circle of radius 5 cm meets a line thro...
To find the length of PQ, we can use the property that a tangent line to a circle is perpendicular to the radius drawn to the point of tangency.

Since OP is a radius of the circle, it is perpendicular to PQ. Therefore, triangle OPQ is a right triangle.

We are given that OQ = 12 cm and OP = 5 cm. Using the Pythagorean theorem, we can find the length of PQ:

PQ^2 = OQ^2 - OP^2
PQ^2 = 12^2 - 5^2
PQ^2 = 144 - 25
PQ^2 = 119

Taking the square root of both sides, we find:

PQ = sqrt(119)

Therefore, the length of PQ is approximately 10.92 cm.

None of the given answer choices match this result, so the correct answer is not provided.
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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 such that OQ = 12 cm. Length PQ isa)12 cmb)13 cmc)8.5 cmd)√119 cmCorrect answer is option 'D'. Can you explain this answer?
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