Question

Three isosceles triangles PBC, QBC and RBC are on the same base, then ______.

Options

• P, Q and R are collinear.

• △PQR is isosceles triangle.

• Q lies on the circumference of a circle with BC as diameter.

• Q is mid-point of line segment PR.

Answer 1

Three isosceles triangles PBC, QBC and RBC are on the same base, then P, Q and R are collinear. 

Explanation:

Steps of construction:

1. Draw a line segment BC.
2. Draw XY, perpendicular bisector of BC.

We know that,

Locus of a point equidistant from two given points is the perpendicular bisector of the line joining the two points.

Thus, any point on the line XY is at equal distance from B and C.

∴ P, Q and R lies on the line XY.