7. Draw a circle of radius 3 cm. From a point 7 cm away from its centre, construct the pair of
tangents to the circle and measure their lengths.
Answers
Answer:
(A) You are Ashraf/Asma, a resident of Lok Vihar, Madhya Pradesh. Due to closure of academic
institutions in your area because of COVID‐19 pandemic, people (students and teachers) are operating
online from their remote locations. The network signals in your colony are quite poor which impacts
the routine functioning of internet, resulting in academic loss.
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=OP2 −OT2
= 72−32= 49−9
=40∴PT=6.3cm(approximately).
