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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.

Grade:12

1 Answers

siddharth gupta
28 Points
7 years ago
use the formula for tangent of half angle of a triangle i.e tan(a/2)=((s-b)(s-c)/s(s-a))1/2 for both half angles.on solving you will obtain s=4c/3.put s=(6+b+c)/2.you will further obtain b=(5c-18)/3..............(1)
Take a=(h,k) and using distance formula calculate b and c.Put b and c in eq.1 and solve.you will get the locus of A.
ON SOLVING YOU MAY ENCOUNTER SOME COMPLICATED EXPRESSIONS .
THE RESULT OBTAINED IS OF THE FORM 
25((h-2)2+k2 )+324-9((h-8)2+k2)=180((h-2)2+k2)1/2
with regards
SIDDHARTH GUPTA

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