Question

Draw a circle of radius $3$cm. From an external point $7$cm away from its centre, construct the pair of tangents to the circle and measure their lengths.

Answer 1

Given: Radius of the circle$=3$cm, OP$=7$cm.

Construction:

(i) With O as the centre draw a circle of radius $3$cm.

(ii) Mark a point P at a distance of $7$cm from O and join OP.

(iii) Draw the perpendicular bisector of OP. Let it meet OP at M.

(iv) With M as centre and MO as radius, draw another circle.

(v) Let the two circles intersect at T and T'.

(vi) Join PT and PT'. They are the required tangents. Length of the tangent, PT$=6.3$cm.

Verification:

In the right angled $\Delta$ OPT,

$PT=\sqrt{O{P}^2-O{T}^2}=\sqrt{7^2-3^2}$

$=\sqrt{49-9}=\sqrt{40}$

$\therefore PT=6.3$cm(approximately).