Answer :

The figure will be drawn as

Since, point A is equidistant from points B and C. We can write in the form,

BA = AC …(i)

Now, length BA =

And length AC =

Substituting lengths BA and AC in equation (i), we get

Squaring both sides, we get

(3 – 0)^{2} + (p – 2)^{2} = (0 – p)^{2} + (2 – 5)^{2}

⇒ 9 + p^{2} + 4 – 4p = p^{2} + 9

⇒ 4p = 4

⇒ p = 1

Hence, the value of p is 1.

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