Coordinates of B(2,0) and C(8,0) are given. If in triangle ABC, 4 tan(A/2) tan(B/2) = 1 ; find equation of locus of point A.


1 Answers

Sandeep Pathak
askIITians Faculty 25 Points
8 years ago
A few results will help solving this problem
\tan\left(\frac{A}{2} \right )=\frac{r}{s-a}\\ \tan\left(\frac{B}{2} \right )=\frac{r}{s-b}\\ sr^2 = (s-a)(s-b)(s-c)
Here, a,b,c are sides of the triangle. s is the semi-radius and r is the in-radius.
Using these equations and given condition, we get 3s=4c which gives (3a+3b=5c).
a=6\\b=\sqrt{(x-8)^2+y^2} \\c=\sqrt{(x-2)^2+y^2}

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