Question

Draw a circle of radius 3 cm. Take two points P and Q on one of its extended diameter each at a distance of 7 cm from its centre. Draw tangents to the circle from these two points P and Q.

Answer 1

Steps of Construction:

Step I: Taking a point O as centre, draw a circle of radius 3 cm.
Step II: Take two points P and Q on one of its extended diameter such that
OP = OQ = 7 cm.

Step III: Bisect OP and OQ and let M₁ and M₂ be the mid-points of OP and OQ respectively.

Step IV: Draw a circle with M₁ as centre and M₁ P as radius to intersect the circle at T₁ and T₂.

Step V: Join PT₁ and PT₂.

Then, PT₁ and PT₂ are the required tangents. Similarly, the tangents QT₃ and QT₄ can be obtained.

Justification:

On joining OT₁, we find ∠PT₁O = 90°, as it is an angle in the semicircle. PT₁ ⊥ OT₁

Since OT₁ is a radius of the given circle, so PT₁ has to be a tangent to the circle.

Similarly, PT₂, QT₃ and QT₄ are also tangents to the circle.