Question

Draw a circle of radius 3 cm, then construct two tangents to the
circle from a point P, 7 cm away from the centre of the circle.
[Only traces of construction required]​

Answer 1

Step-by-step explanation:

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=OP2−OT2=72−32

=49−9=40

∴PT=6.3cm(approximately).

Answer 2

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