tmua.me Extreme Set A Paper 2 · Question 15

The vertices of a convex quadrilateral are $A,B,C,D$ , in that order. A point $P$ in the plane is called balanced if

PA^2+PC^2=PB^2+PD^2.

Consider the condition that every point on the diagonal $AC$ is balanced, and the statement that $ABCD$ is a rectangle.

Which of the following correctly describes the condition in relation to the statement?

A quadrilateral is convex if each of its interior angles is less than $180^\circ$ .

AThe condition is necessary but not sufficient.

BThe condition is sufficient but not necessary.

CThe condition is both necessary and sufficient.

DThe condition is neither necessary nor sufficient.

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