Trigonometry & Inverse Trigonometry
Triangle Circumscribed about Circle
Grade 11
Question:
<p>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 will be a</p>
<p>(a) straight line parallel to side BC</p>
<p>(b) straight line at right angle to side BC</p>
Step-by-Step Solution
Key Concept: Use properties of circumscribed triangles and the constraint on the product of segments to determine the locus.
<p>For a triangle circumscribed about a fixed circle of radius 1, when BC is fixed in direction and touches the circle at D with the constraint BD·CD = 2, the locus of vertex A is a straight line. Using properties of tangent circles and the given constraint, this locus is parallel to the fixed side BC.</p>
Correct Answer: A