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 : (A) 12 cm. (B) 13 cm (C) 8.5 cm (D) cm

Answer 1

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$\bold{Dear\:user!!}$



$\bold{\underline{Question-}}$

seems like a mistake in your question the correct question is 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 : (A) 12 cm. (B) 13 cm (C) 8.5 cm (D) √119cm



$\bold{\underline{Answer-}}$



$\bold{Your\:answer\:is\:option\:(D. )}$




$\bold{\underline{Explanation-}}$ According to the question we know that A tangent is PQ at a point of p of the circle at the radius 5cm meets a line through the centre O at point Q and OQ = 12


Need to find length PQ


now,



in ΔPOQ


Here angle P is right angle and we know that right angle is always 90°


so,


Using the Pythagoras theorem



OQ² = PQ² + OP²



now, transfer the PQ² in right side


PQ² = OQ² - OP²


now, putting the above values we get


PQ² = (12)² - (5)²



PQ² = 144 - 25



PQ² = 119



PQ = √119



Hence, the correct answer is √119








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