If a point A(0,2) is equidistant from the points B(3,p) and C(p,5), then find the value of p.

Distance between two points = √(x₂-x₁)²(y₂-y₁)²
∴AB = √(0-3)²+(2-p)² ⇒ √9+4-4p+p² ⇒ √p²-4p+13
∴AC = √(p-0)²+(5-2)² ⇒ √p²+9
As given AB=AC
⇒√p²-4p+13 = √p²+9
Squaring both sides
⇒p²-4p+13 = p²+9
⇒-4p = 9-13
⇒-4p = -4
⇒p = -4/-4 = 1