Question

Construct a circle whose radius is equal to 4.2 cm. Let P be a point whose distance from its centre is 6.5 cm. Construct two tangents to it from P and measure their lengths.

Answer 1

Steps of Construction:
Step I : Take a point O and draw a circle of radius 4.2 cm.
Step II : Take a point P at a distance of 6.5 cm from the centre O
Step III : Join OP and bisect it. Let M be the mid-point.
Step IV : With M as centre and MP as radius, draw a circle to intersect the circle
at Q and R.
Step V : Join PQ and PR. Then, PQ and PR are the required tangents.
On measuring, we find, PQ = PR = 4.9 cm.

Justification:
On joining OQ, we find that ∠PQO = 90°, as ∠PQO is the angle in the semicircle.
∴ PQ ⊥ OQ
Since OQ is the radius of the given circle, so PQ has to be a
tangent to the circle. Similarly, PR is also a tangent to the circle.