Question

a point P is 5 cm from the centre of the circle the length of the tangent from the point P to the circle is 8cm, find the radius of the circle.​

Answer 1

Answer:

Let the centre of a circle be O.

Let the tangent be PQ.

so,

PO = 5 cm

PQ = 6 cm

As radius is perpendicular to tangent at point of contact

So, angle OQP = 90 degree

By Pythagoras Theorem,

(OP)2 = (OQ)2 + (PQ)2

132 = (OQ)2 + 122

169 - 144 = (OQ)2

(OQ)2 = 25

OQ = 5 cm

Radius ofthe circle is 5 cm.

Answer 2

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Let the centre of a circle be O.

Let the tangent be PQ.

so,

PO = 5 cm

PQ = 6 cm

As radius is perpendicular to tangent at point of contact

So, angle OQP = 90 degree

By Pythagoras Theorem,

(OP)2 = (OQ)2 + (PQ)2

132 = (OQ)2 + 122

169 - 144 = (OQ)2

(OQ)2 = 25

OQ = 5 cm

Radius ofthe circle is 5 cm.