The base `B C` of ` A B C` is fixed and the vertex `A` moves, satisfying the condition `cot(B/2)+cot(C/2)=2cot(A/2),` then (a) `b+c=a` (b) `b+c=2a` (c) vertex `A` moves along a straight line (d) Vertex `A` moves along an ellipse

Options

A. `b + c = a`
B. `b + c = 2a`
C. vertex A moves along a straight line
D. vertex A moves along an ellipse

Answer

B, D

Explanation

Given `(s(s-b))/(Delta) + ((s-c))/(Delta) = (2s(s-a))/(Delta)`
`rArr s-b + s - c = 2 (s-a)`
`rArr b+c = 2a`
So, locus of vertex A is an ellipse