2016 · Q71
Let ABC be a triangle in which AB = AC. Let L be the locus of points X inside or on the triangle such that BX = CX. Which of the following statements are correct?
- 1L is a straight line passing through A and in-centre of triangle ABC is on L.
- 2L is a straight line passing through A and orthocentre of triangle ABC is a point on L.
- 3L is a straight line passing through A and centroid of triangle ABC is a point on L.
Select the correct answer using the codegiven below.
Elementary MathematicsGeometry: Lines, Angles and Triangles
- A1 and 2 only
- B2 and 3 only
- C1 and 3 only
- D1, 2 and 3
Explanation
For AB = AC, the locus BX = CX is the perpendicular bisector of BC. This line is the symmetry axis of the triangle through A. The in-centre, orthocentre and centroid of an isosceles triangle all lie on this axis. So all three statements hold — option D.