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

Open in App

Solution

given data:

PQ = 24 cm

OQ = 25 cm

OP = radius = ?

P is a point of contact , at point of contact , tangent and radius are perpendicular to each other.

Therefore triangle is right angled triangle angle OPQ = 90°

BY pythagoras theorem,

OP = 7 cm

Therefore , OP = radius = 7 cm

Suggest Corrections

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. 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 .

Join BYJU'S Learning Program

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

given data: PQ = 24 cm OQ = 25 cm OP = radius = ? P is a point of contact , at point of contact , tangent and radius are perpendicular to each other. Therefore triangle is right angled triangle angle OPQ = 90° BY pythagoras theorem, OP = 7 cm Therefore , OP = radius = 7 cm

given data:

PQ = 24 cm

OQ = 25 cm

OP = radius = ?

P is a point of contact , at point of contact , tangent and radius are perpendicular to each other.

Therefore triangle is right angled triangle angle OPQ = 90°

BY pythagoras theorem,

OP = 7 cm

Therefore , OP = radius = 7 cm