A variable triangle is circumscribed about a fixed circle of unit radius

MATHEMATICS · Single correct · CBSE · Mathematics · Circles · Circles

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)(CD)=2

, then the locus of vertex

A

is a straight line (1) parallel to side

BC

(2) at right angles to side

BC

(3) making an angle

\frac{\pi}{6}

with

BC

(4) making an angle

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

with

BC