Question

Draw a circle of radius 6 cm. From a point 10 cm away from its centre, construct a pair of tangents to the circle and find their lengths.

• A. 8 cm, 8 cm
• B. 5 cm, 7 cm
• C. 2 cm, 5 cm
• D. 3 cm, 8 cm

Answer 1

The correct option is A

8 cm, 8 cm

Draw a circle of radius 6 cm and mark its centre as O.

Draw a line segment OP = 10 cm.

Construct the perpendicular bisector of OP which intersects OP at point O’.

Take O’P as radius and draw another circle. Let it intersect the first circle at Q and R.

Join PQ and PR and measure them.

PQ = PR = 8 cm

Verify using Pythagoras theorem:

$P{Q}^2=O{P}^2-O{Q}^2$

$={10}^2-6^2$

$=100-36=64$

Or, $PQ=8cm$