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Question
Use ruler and compass only for answering this question.
Draw a circle of radius 4 cm. Mark the centre as O. Mark a point P outside the circle at a distance of 7 cm from the centre. Construct two tangents to the circle from the external point P.
Measure and write down the length of any one tangent.
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Solution
Steps of Construction:
- Draw a circle with centre O and radius 4 cm using a compass.
- Mark a point P on a horizontal line such that OP = 7 cm.
- Join OP.
- Draw the perpendicular bisector of OP to obtain its midpoint, say M.
- With M as centre and radius MO, draw a circle.
- This circle will cut the given circle at two distinct points A and B.
- Join PA and PB.
- PA and PB are the required tangents from the external point P to the given circle.
Measure the length of the tangent.
Length of tangent
`sqrt(OP^2 − "radius"^2)`
= `sqrt(7^2 − 4^2)`
= `sqrt(49 − 16)`
= `sqrt(33)`
= 5.74 cm (approximately)
So, the length of one tangent is 5.74 cm.
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