3 Construct a pair of tangents to a circle of radius 2.5cm from an external point which is at a distance of 6cm from the centre of the circle. Write the steps of construction
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Answer:
Given: Radius of the circle=3cm, OP=7cm.
Construction:
(i) With O as the centre draw a circle of radius 3cm.
(ii) Mark a point P at a distance of 7cm from O and join OP.
(iii) Draw the perpendicular bisector of OP. Let it meet OP at M.
(iv) With M as centre and MO as radius, draw another circle.
(v) Let the two circles intersect at T and T'.
(vi) Join PT and PT'. They are the required tangents. Length of the tangent, PT=6.3cm.
Verification:
In the right angled Δ OPT,
PT=
OP
2
−OT
2
=
7
2
−3
2
=
49−9
=
40
∴PT=6.3cm(approximately).
Step-by-step explanation:
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