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What is the distance between the points of tangency of a common tangent AB to two circles I and II which are externally tangent to each other. The radii of the two circles are 9 and 16 units.
What Is The Distance Between The Points Of Tangency Of A Com...

 


Options:
A .   24
B .   22
C .   27
D .   173
Answer: Option A
:
A

What Is The Distance Between The Points Of Tangency Of A Com...
From the diagram above, AC1=16
and BC2=9.
Also C1 - C2=25.
PC1 = 7 (16-9)
AB=PC2
C1 - P - C2 is a right angled triangle
(C1C2)2 = PC12+PC22 
Thus, PC2 =62549
= 576 = 24 



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