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:

1. Firstly, we draw a circle with centre O and radius 6 cm.

2. Mark a point P at a distance of OP = 10 cm, and join OP.

3. Draw a right bisector of OP, intersecting OP at Q.

4. Now, taking Q as centre and radius OQ = PQ, draw a circle to intersect the given circle at T and T$.

5. Join PT and P$T$ to obtain the required tangents.

Thus, PT and P$T$ are the required tangents.

To find the length of the tangents.

We know that OT ⊥ PT and ΔOPT is the right triangle.

Therefore, OT = 6 cm (radius) and PO = 10 cm.

So, in ΔOPT,

PT2 = OP2 − OT2 [By Pythagoras theorem]

= (10)2 − (6)2

= 100 – 36

= 64

PT = 8 cm

Therefore, the length of tangents 8 cm each.