Mathematics
Two circles of radii 8 cm and 3 cm have a direct common tangent of length 10 cm. Find the distance between their centres, up to two places of decimal.
Circles
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Answer
Let there be two circles with centre A and B with radius 8 cm and 3 cm respectively.
Let TT' be the length of common tangent.
Construct a right-angled triangle Δ ADB by drawing a line from center B parallel to TT' to intersect radius AT at D.
From figure,
⇒ TT' = BD = 10 cm
⇒ DT = BT' = 3 cm.
⇒ AD = AT - DT = 8 - 3 = 5 cm.
In right angled triangle ADB,
⇒ AB2 = AD2 + DB2
⇒ AB2 = 102 + 52
⇒ AB2 = 100 + 25
⇒ AB2 = 125
⇒ AB =
⇒ AB = 11.18 cm.
Hence, the distance between the centres 11.18 cm.
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