Question

A tangent PQ at a point P of a circle of radius 6cm meets a line through the centre O at a point Q so that OQ =10cm. Length of tangent PQ

Answer 1

This is ur answer buddy ❤️

Answer 2

The length of tangent PQ is 8cm.

A tangent PQ at a point P of a circle of radius 6 cm meets a line through the centre O at a point Q so that OQ = 10cm.

We have to find the length of tangent PQ.

see diagram, we have drawn a circle of centre O. a tangent is drawn at a point P of circle meets a line through the centre O at a point Q.

we know,

“A tangent is perpendicular on the radius of circle.”

∴ ∆OPQ is a right angled triangle,

using Pythagoras theorem,

OQ² = OP² + PQ²

⇒(10cm)² = (6cm)² + PQ²

⇒PQ² = 100cm² - 36cm² = 64cm²

⇒PQ = 8 cm

Therefore the length of tangent PQ is 8cm.