Question

Draw a circle of radius 3 cm. Take two points P and Q on one of its diameters extended on both sides, each at a distance of 7 cm on opposite sides of its centre. Draw tangents to the circle from these two points P and Q.

Answer 1

Follow the given steps to draw the tangents to the circles from the two points P and Q:

Step 1. Draw a circle with centre O and radius 3 cm.

Step 2. Extend its diameter on both sides and mark two points P and Q on it such that OP = OQ = 7 cm.

Step 3. Draw the perpendicular bisectors of OP and OQ. Let R and S be the mid-points of OP and OQ, respectively.

Step 4. Draw a circle with R as centre and radius PR, to intersect the circle with centre O at the points T and T'.

Step 5. Draw another circle with S as centre and radius SQ, to intersect the circle with centre O at the points B and B'.

Step 6. Join PT and PT'. Also, join QB and QB'.

Here, PT and PT' are the tangents to the circle from P. Also, QB and QB' are the tangents to the circle from Q.