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A variable triangle A B C is circumscrib...

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. (a)parallel to side BC (b)perpendicular to side BC (c)making an angle `(pi/6)` with BC (d) making an angle `sin^(-1)(2/3)` with `B C`

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To solve the problem, we need to analyze the given conditions and derive the locus of vertex A of triangle ABC that is circumscribed about a fixed circle of unit radius. ### Step-by-Step Solution: 1. **Understanding the Configuration**: - We have a triangle ABC circumscribed about a fixed circle (incircle) with a radius of 1 unit. - The side BC touches the circle at point D, and the lengths BD and CD are given to be equal to 2. ...
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