KVPY2017MathematicsStraight Lines
Let BC be a fixed line segment in the plane. The locus of a point A such that the triangle ABC is isosceles, is (with finitely many possible exceptional points)
Options
- Aa line
- Ba circle
- Cthe union of a circle and a line
- Dthe union of two circles and a line
Correct answer
D. the union of two circles and a line
Step-by-step solution
Case (i): If B = C locus of A is bisector of BC So it is straight line Case (ii): If A = C BC fixed B ( a , 0), C (0, a ) BC = AB So, (x-a)²+y²=2 a² Circle Case (iii): array l A = B AC = BC h ²+( k - a )² = 2 a ² x ²+( y - a )²=2 a ² array also a circle So union of two circle and a line.