If a point A(0, 2) is equidistant from the points

It is given that A(0, 2) is equidistant from the points B(3, p) and C(p, 5).

∴ AB = AC

$\Rightarrow \sqrt{(3-0)^{2}+(p-2)^{2}}=\sqrt{(p-0)^{2}+(5-2)^{2}}$ (Distance formula)

Squaring on both sides, we get

$9+p^{2}-4 p+4=p^{2}+9$

$\Rightarrow-4 p+4=0$

$\Rightarrow p=1$

Thus, the value of p is 1.