Question

Construct two tangents to a circle of radius 4.5 cm from a point 2.5 cm away from the circle.

Answer 1

Length of the radius = 4.5 cm

Point P is at a distance of 2.5 cm from the circle. This means that the point is at a distance of 4.5 + 2.5 = 7 cm from the centre of the circle.

The steps below need to be followed to construct the circle and the tangents.

1. Draw a circle of radius 4.5 cm with centre O.

2. Mark a point P at a distance of 7 cm from the centre of the circle.

3. Join OP.

4. Draw the perpendicular bisector of OP such that it divides OP into two equal parts at M.

5. With M as the centre and OM as the radius, draw a circle that cuts the previously drawn circle at points X and Y.

6. Join PX and PY.

Thus, PX and PY are tangents to the circle of radius 4.5 cm from a point 2.5 cm away from the circle.