Question

Draw a circle of diameter 9 cm. Mark a point at a distance of 7.5 cm from the centre of the circle. Draw tangents to the given cirlce from this exterior point. Measure the length of each tangent.

Answer 1

Draw a circle with radius 4.5 cm and centre O.

Draw a line segment OP = 7.5 cm
Make perpendicular bisector of OP which intersects OP at point O’.
Take O’P as radius and draw another circle.
From point P, draw tangents to points of intersection between the two circles.

If Q and R are points of intersection , then

$P{Q}^2=7.5²-4.5²$
$P{Q}^2=36PQ=\sqrt{36}PQ=6$


∴PQ=PR=6 cm