Hello, ailmasum!
Who assigned this problem?
It's truly silly . . .
$\displaystyle \text{Given points }A(0, 14),\;B(18, 4).$
$\displaystyle \text{Find a third point }C\text{ so that }\Delta ABC\text{ is an isosceles triangle.}$
Code:

 ♥ B
 ♥ o
 ♥ *
 ♥ *
  +     ♥ *   
 *
 * ♥
 * ♥
 * ♥
o ♥

$\displaystyle \,C$ can be (almost) any point on the perpendicular bisector of $\displaystyle AB.$
Code:
* * *
* * B
* o
* * *
*
* A * *
* o *
* (0,14) *
* *
* *
* *
* * *
Consider the circle with center $\displaystyle \,A$ and radius $\displaystyle AB.$
$\displaystyle \,C$ can be (almost) any point on the circle.
Code:
* * *
* *
* *
* *
* B *
* o(18,4) *
* * *
*
* * *
o *
A * *
* * *
Consider the circle with center $\displaystyle \,B$ and radius $\displaystyle AB.$
$\displaystyle \,C$ can be (almost) any point on the circle.