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Question
Draw two circles of radii 3 cm and 3.5 cm, their centres being 8 cm apart. Construct a transverse common tangent and measure its length.
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Solution
Steps of construction:
(i) Draw a line OP= 8 cm.
(ii) At O, draw a circle of radius 3 cm.
(iii) At P, draw a circle of radius 3.5 cm.
(iv) At O, draw a third circle concentric to the smaller circle and radius= (3.5 + 3) cm= 6.5 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 ci rel es intersect each other.
(vii) Join OT and OS to meet the smaller circle at A and B.
(viii) Join PT and PS.
(ix) On PT and PS, draw perpendiculars to meet the bigger circle at M and N.
(x) Join AM and BN.
AM and BN are the required tangents.
On measuring, AM= BN = 8 cm.
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