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Question
Draw the two tangents from a point which is 10 cm away from the centre of a circle of radius 5 cm. Also, measure the lengths of the tangents.
Solution
Radius = 5 cm, Distance = 10 cm
Steps of construction:
1. With O as centre, draw a circle of radius 5 cm.
2. Draw a line OP = 10 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 circle at A and B.
5. Join AP and BP. AP and BP are the required tangents.
Verification: In the right ∆OAP
PA2 = OP2 – OA2
= 102 – 52
= `sqrt(100 - 25)`
= `sqrt(75)`
= 8.7 cm
Length of the tangent is = 8.7 cm
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