Question

Draw a circle of radius 6cm.From a point 10 cm away from its center, construct the pair of Tangents to the circle and measure their lengths?
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Answer 1

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Answer 2

Answer:

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 PT

to obtain 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