Question

Draw a circle of radius 3 cm. From a point P, 7 cm away from its centre draw two tangents to the circle. Measure the length of each tangent.

Answer 1

Steps of Construction:

Step 1: Draw a circle with O as center and radius 3 cm.

Step 2: Mark a point P outside the circle such that OP = 7cm.

Step 3: Join OP. Draw the perpendicular bisector XY of OP. cutting OP at Q.

Step 4: Draw a circle with Q as center and radius PQ (or OQ), to intersect the given circle at the points T and T’.

Step 5: Join PT and PT’.

Here, PT and PT’ are the required tangents.

PT = PT ' = 6.3cm (Approx.)

Answer 2

Steps of construction :

1. Draw a line segment PO = 7 cm.

2. From the point O, draw a circle of radius = 3 cm.

3. Draw a perpendicular bisector of PO. Let M be the mid-point of PO.

4. Taking M as centre and OM as radius draw a circle.

5. Let this circle intersects the given circle at the point Q and R.

6. Join PQ and PR.

On measuring we get 

PQ = PR = 6.3 cm