Question

A line through the centre of radius 7cm cuts the tangent, at a point P on the circle, kyon such that PQ = 24 cm . Find OQ.​

Answer 1

Step-by-step explanation:

OP = 7cm = radius

PQ= 24cm

OQ= OP+ PQ

OQ= 7+24

OQ= 31 cm

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Answer 2

$\huge{\underline{\bf{Given}}}$

• Radius (OP) = 7cm
• PQ = 24cm

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$\huge{\underline{\bf{To\: find}}}$

• Length of OQ.

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$\huge{\underline{\bf{Solution}}}$

※ Since tangent at a point on a circle is perpendicular to the radius through the point.

Therefore, OP is perpendicular to PQ.

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In right triangle OPQ, we have

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$\: \: \: \: \: \: \: \: \: \: \: \: \boxed{\tt{\bigstar{By\: Pythagoras\: Theorem{\bigstar}}}}$

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$\tt\longmapsto{OQ^2 = OP^2 + PQ^2}$

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$\tt\longmapsto{OQ^2 = (7)^2 + (24)^2}$

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$\tt\longmapsto{OQ^2 = 49 + 576}$

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$\tt\longmapsto{OQ^2 = 625}$

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$\tt\longmapsto{OQ = \sqrt{625}}$

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$\tt\longmapsto{OQ = 25cm}$

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★ Hence, Hypotenuse OQ is 25 cm.

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