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13.    A rhombus is inscribed in the region common to the two circles x2 + y2 – 4x -12 = 0 and x2 + y2 + 4x – 12 = 0 with two of its vertices on the line joining the centre of the circles. The area of the rhombus is


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Deepak Patra , 11 Years ago
Grade upto college level
anser 1 Answers
Jitender Singh

Last Activity: 10 Years ago

Ans:8\sqrt{3}
Sol:
Let p & q be the diagonals of the rhombus. Then area A of rhombus is
A = \frac{p.q}{2}
Rhombus is only possible in the commom region of two circles with p as line joining centres of two circles & q be the common chord of two circles.
p = 4
q = 4\sqrt{3}
A = 8\sqrt{3}
Thanks & Regards
Jitender Singh
IIT Delhi
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