Question

Draw the two tangents from a point which is 10 cm away from the centre of a circle of radius 5 cm. Also, measure the lengths of the tangents.

Answer 1

Radius = 5 cm

The distance between the point from the centre is 10 cm.

Construction:

Steps:

(1) With O as centre, draw a circle of radius 5 cm.

(2) Draw a line OP =10 cm.

(3) Draw a perpendicular bisector of OP which cuts OP at M.

(4) With M as centre and MO as radius, draw a circle which cuts previous circle at A and B.

(5) Join AP and BP. AP and BP are the required tangents. Thus length of the tangents are PA and PB = 8.7 cm.

Verification:

In the right triangle ∠POA;