Problem

A variable triangle

ABC

is circumscribed about a fixed circle of unit radius. Side

BC

always touches the circle at

D

and has fixed direction. If

B

and

C

vary in such a way that

(BD) \cdot (CD) = 2

, then locus of vertex

A

will be a straight line a. parallel to side

BC

b. right angle to side

BC

c. making an angle

\frac{\pi}{6}

with

BC

d. making an angle

\sin^{-1}\left(\frac{2}{3}\right)

with

BC