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Question
Take a point which is 11 cm away from the centre of a circle of radius 4 cm and draw the two tangents to the circle from that point.
Solution
Radius = 4 cm, Distance = 11 cm
Steps of construction:
1. With O as centre, draw a circle of radius 4 cm.
2. Draw a line OP = 11 cm.
3. Draw a perpendicular bisector of OP, which cuts OP at M.
4. With M as centre and MO as radius, draw a circle which cuts the previous circles A and B.
5. Join AP and BP. AP and BP are the required tangents.
This the length of the tangents PA = PB = 10.2 cm
Verification: In the right angle triangle OAP
PA2 = OP2 – OA2
= 112 – 42
= 121 – 16
= 105
PA = `sqrt(105)`
= 10.2 cm
Length of the tangents = 10.2 cm
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