A variable triangle `A B C` is circumscribed about a fixed circle of unit radius. Side `B C` always touches the circle at D and has fixed direction. If B and C vary in such a way that (BD) (CD)=2, then locus of vertex A will be a straight line. parallel to side BC perpendicular to side BC making an angle `(pi/6)` with BC making an angle `sin^(-1)(2/3)` with `B C`

Explanation

Here, `BD = s-b`

`CD = s-c`

`BD*CD = (s-b)(s-c)`

`=>2 = (s-b)(s-c)`

`=>2s(s-a) = s(s-a)(s-b)(s-c)`

`=>2s(s-a) = Delta^2`

`=>Delta^2/s^2 = (2(s-a))/s`

`=>r^2 = 2-(2a)/s`

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