tmua.me Extreme Set A Paper 2 · Question 2

A triangle $ABC$ has $AB=3$ , $AC=4$ and $BC=c$ .

Consider the condition

c\leq3\sqrt2

and the statement

AP^2\geq BP\cdot PC\qquad\text{for every point }P\text{ on the line segment }BC.

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

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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