Question

Draw a circle of radius 3cm. Mark a point P at a distance 7.5cm away from the centre. Draw tangents from P to the circle ​

Answer 1

Answer:

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

Construction:

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

(ii) Mark a point P at a distance of 7cm 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=6.3cm.

Verification:

In the right angled Δ OPT,

PT=

OP

2

−OT

2

=

7

2

−3

2

=

49−9

=

40

∴PT=6.3cm(approximately).