Question

PQ and PR are the tangents to the circle with centre o and radius 5cm . if op =13 cm . find length of the tangent. class10​

Answer 1

hope this helps you mate

Answer 2

Given :

PQ and PR are two tangents from point P .

Radius of circle = 5 cm

Length of OP = 13 cm

To find :

The length of the tangents .

Solution :

The tangent on a circle makes 90° angle with the perpendicular drawn from the center of the circle .

Now , In ΔPOR ,

OP = 13 cm

OR = 5 cm {radius}

∠PRO = 90°

using , Pythagoras theorem ,

OP^2 = OR^2 + PR^2

=> 13 * 13 = 5 * 5 = PR^2

=> PR^2 = 144

=> PR = 12 cm

As PR and PQ and tangents from same external point , their lengths will be equal .

PR = PQ = 12 cm .

The length of the tangents PQ = PR = 12 cm .