Question

In a right angled triangle, the point of intersection of perpendicular bisectors of sides is _________.

• A. Midpoint of the hypotenuse
• B. External point of a triangle
• C. Internal point of a triangle
• D. Midpoint of the base

Answer 1

Answer: (A)

Midpoint of the hypotenuse

In a right-angled triangle, the point of intersection of perpendicular bisectors of sides is the midpoint of the hypotenuse.

Imagine a triangle $△ABC$.

Let $O$ be the circumcenter, then $O$ can lie on the line $BC$.

If $OB=OC$ by definition of the circumcenter i.e. $O$ must be the midpoint of the segment $BC$.

In that case $\angle A={90}^{\circ }$, since it subtends diameter $BC$.