A tangent is drawn at a point P on a circle. A line through the centre O of a circle of radius 7 cm cuts the tangent at Q such that PQ = 24 cm. Find OQ.

10 cm

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15 cm

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20 cm

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25 cm

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Solution

The correct option is D
25 cm

Since tangent at a point on the circle is perpendicular to the radius through that point of contact.

$∴ O P ⊥ O Q$

$In right angled triangle OPQ,$

${O Q}^{2} = {O P}^{2} + {P Q}^{2} (By Pythagoras theorem)$

${O Q}^{2} = 7^{2} + 24^{2}$

${O Q}^{2} = 49 + 576$

${O Q}^{2} = 625$

$O Q = \sqrt{625} = 25 c m$

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Similar questions

A tangent is drawn at a point P on a circle. A line through the centre O of a circle of radius 7 cm cuts the tangent at Q such that PQ = 24 cm. Find OQ.

Q. If the tangent at a point P to a circle with centre O cuts a line through O at Q such that PQ = 24 cm and OQ = 25 cm. Find the radius of the circle.

Q. A line through the centre

O

of a circle of radius

7 c m

cuts the tangent, at a point

P

on the circle, at

Q

such that

P Q = 24 c m .

Find

O Q .

Q. A tangent

P Q

at a point

P

of a circle of radius

5 c m

meets a line through the centre

O

so that

O Q = 13 c m .

Find the length of

P Q .

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A tangent is drawn at a point P on a circle. A line through the centre O of a circle of radius 7 cm cuts the tangent at Q such that PQ = 24 cm. Find OQ.

The correct option is D 25 cm Since tangent at a point on the circle is perpendicular to the radius through that point of contact. ∴OP⊥OQ In right angled triangle OPQ, OQ2=OP2+PQ2 (By Pythagoras theorem) OQ2=72+242 OQ2=49+576 OQ2=625 OQ=√625=25 cm