tmua.me Extreme Set A Paper 2 · Question 4

In the coordinate plane, let

O=(0,0),\quad A=(1,0),\quad B=\left(-\frac12,\frac{\sqrt3}{2}\right),\quad C=\left(-\frac12,-\frac{\sqrt3}{2}\right).

A point $P$ lies on the circle

x^2+y^2-4x+2y+1=0.

Whenever the three lengths $PA$ , $PB$ and $PC$ can be used as the side lengths of a triangle of positive area, let $K(P)$ be the area of that triangle.

What is the greatest possible value of $K(P)$ ?

\sqrt{15}-2\sqrt3

\dfrac{2\sqrt3+\sqrt{15}}2

\dfrac{9\sqrt3+4\sqrt{15}}4

\sqrt3+\sqrt{15}

2\sqrt3+\sqrt{15}

4\sqrt3+2\sqrt{15}

examday

tmua.me Extreme Set A Paper 2 · Q4