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Question

Area of the hexagon formed by points of contact of direct common tangents to the circle (x1)2+(y3)2=9, (x7)2+(y+5)2=25 with the two centres is
  1. 306 sq. units  
  2. 456 sq. units 
  3. 256 sq. units 
  4. 326 sq. units  


Solution

The correct option is D 326 sq. units  
Given circles are 
(x1)2+(y3)2=9, (x7)2+(y+5)2=25
The centre and radius are
C1(1,3)      r1=3
C2(7,5)   r2=5


d=C1C2=62+82=10
Length of D.C.T
AB=CD=d2(r2r1)2=1004=46

Area of hexagon AC1CDC2B
=2×area of trapezium AC1C2B=2×12(3+5)×(46)=326 sq. units

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