Question

Draw a circle of radius 3 cm. Take two point P and Q on its diameter produced at the equal distances of 7 cm from its center. Draw two tangents to the circle from these two points.

Answer 1

Given :

A circle with radius 3 cm.

Two points P and Q on its diameter produced at equal distance of 7 cm from its center. 

i.e., OP = OQ = 7 cm

Steps of construction :

(1) Draw a circle with radius 3 cm.

(2) Draw the diameter AB and produce it to point P and Q of the either side of circle such that OP = OQ = 7 cm.

(3) Draw the perpendicular bisectors of OP and QQ which intersect them of M₁ and M₂ respectively.

(4) Taking M₁ as centre and radius M₁O draw a circle which intersects the given circle at T₁ and T₂.

(5) Join PT₁ and PT₂.

(6) Taking M₂ as centre and radius M₂O draw another circle which intersects the given circle at S₁ and S₂.

(7) Join QS₁ and QS₂.

Hence PT₁, PT₂, QS₁ and QS₂ are the required tangents.