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 measure their lengths.

Answer 1

Steps of Construction:
Step I: With O as a centre and radius equal to 6 cm, a circle is drawn.
Step II: A point P at a distance of 10 cm from the centre O is taken. OP is joined.

Step III: Perpendicular bisector of OP is drawn and it intersects OP at M.
Step IV: With M as a centre and OM as a radius, a circle is drawn intersecting the previous circle at Q and R.
Step V: PQ and PR are joined.
Thus, PQ and PR are the tangents to the circle.
On measuring the length, tangents are equal to 8 cm.
PQ = PR = 8cm.
Justification:
OQ is joined.
$\angle PQO={90}^{\circ }$ (Angle in the semi-circle)
$\therefore OQ\perp PQ$
Therefore, OQ is the radius of the circle then PQ has to be a tangent of the circle.
Similarly, PR is a tangent of the circle.