Mathematics
Two circles of radii 18 cm and 8 cm touch externally. Find the length of a direct common tangent to the two circles.
Circles
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Answer
Let there be two circles with centre A and B with radius 18 cm and 8 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,
DT = BT' = 8cm.
AD = AT - DT = 18 - 8 = 10 cm.
AB = 18 + 8 = 26 cm
In right angled triangle ADB,
⇒ AB2 = AD2 + DB2
⇒ 262 = 102 + DB2
⇒ 676 = 100 + DB2
⇒ DB2 = 676 - 100
⇒ DB2 = 576
⇒ DB = 24 cm
Since, TDBT' is a rectangle,
So, TT' = DB = 24 cm.
Hence, the length of direct common tangent is 24 cm.
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