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Question
Draw two circles of radii 2.5 cm and 3.5 cm respectively so that their centres are 8 cm apart. Draw direct comm on tangents to the circle.
Solution
Steps of construction:
(i) Draw a line OP= 8 cm.
(ii) At O, draw a circle of radius 3.5 cm.
(iii) At P, draw a circle of radius 2.5 cm.
(iv) At O, draw a third circle concentric to the bigger circle
and radius = (3.5 - 2.5) cm= 1 cm
(v) Draw a perpendicular bisector of OP. Let R be the mid-point of OP.
(vi) With R as centre and OR as radii, draw a fourth circle. Mark as T and S where the third and fourth circles intersect each other.
(vii) Join OT and OS and extend lines to meet the bigger circle at A and B.
(viii) Join PT and PS.
(ix) On PT and PS, draw perpendiculars to meet the smaller cirde at Mand N.
(x) Join AM and BN.
AM and BN are the required tangents.
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