how to prove appolonius theoram using geometry??

Dear Anshu Dhamiwal,

Ans:- Consider the given figure:-

In the above fig. θ'=∏-θ

b²=m²+d²-2md cosθ..................(1)

c²=m²+d²-2md cosθ'

=m²+d²+2md cosθ       (as cos(∏-A)= - cosA) ..................(2)

adding 1 && 2 we get

b²+c²=m²+d² (proved)

(WE HAVE TO USE A LITTLE AMOUNT OF TRIGO TO PROVE IT)

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Soumyajit Das IIT Kharagpur