Question

find the length of the tangent to a circle from a point 13cm away from the centre of the circle of radius 5cm​

Answer 1

Answer:

Consider a circle with centre O.

OP = radius = 5 cm.

A tangent is drawn at point P, such that line through O intersects it at Q.

And, OQ = 13cm (given).

To find:

Length of tangent PQ =?

We know that tangent and radius are perpendicular to each other.

∆OPQ is right angled triangle with ∠OPQ = 90°

By Pythagoras theorem we have,

OQ²= OP² + PQ²

OQ²= OP² + PQ² ⇒ 13² = 5²+ PQ²

+ PQ²⇒ PQ² = 169 – 25 = 144

+ PQ²⇒ PQ² = 169 – 25 = 144 ⇒ PQ = √114

= 12 cm

= 12 cm Therefore, the length of tangent = 12 cm.