Q. 55.0( 6 Votes )

# A circle with cen

Let the diagram be as follows:

P divides the line AB in the ratio 3:1

Adding 1 both side, we get

BP = 2 cm

And hence,

AP = 3BP = 3(2) = 6 cm

Let the centre be O.

From this figure it can be interpreted that OP will be the radius of the circle.

Radius OP is perpendicular to the tangent AB as radius is perpendicular to the tangent.

If OP is to AB which implies that OP is AP and OP is PB.

Hence Δ OPA is right angled triangle

OPA = 90°

OA2 = AP2 + OP2

OP2 = OA2 – AP2

OP2 = 102 – 62

OP2 = 100 – 36

OP2 = 64

OP = 8 cm

Therefore the radius of circle = 8 cm.

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