Mathematics
Calculate the length of a direct common tangent to two circles of radii 3 cm and 8 cm with their centres 13 cm apart.
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.
From figure,
DT = BT' = 3cm.
AD = AT - DT = 8 - 3 = 5 cm.
In right angled triangle ADB
Since, TDBT' is a rectangle,
So, TT' = DB = 12 cm.
Hence, the length of direct common tangent is 12 cm.
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