\

The vertices of equilateral triangle are $\"\"$ and $\"\"$ .

\

Let the third vertex of the triangle be $\"\"$ .

\

Find the lengths of sides of the triangle.

\

$\"\"$ .

\

$\"\"$ .

\

$\"\"$

\

$\"\"$ .

\

\

All three sides have the equal lengths.

\

$\"\"$ .

\

Consider $\"\"$ .

\

$\"\"$ equation $\"\"$ .

\

Consider $\"\"$ .

\

$\"\"$ equation $\"\"$ .

\

Solve the equation $\"\"$ .

\

$\"\"$

\

Square on both sides.

\

$\"\"$

\

$\"\"$

\

$\"\"$

\

$\"\"$ .

\

Substitute $\"\"$ in equation $\"\"$ .

\

$\"\"$

\

$\"\"$

\

Square on both sides.

\

$\"\"$

\

$\"\"$

\

$\"\"$

\

$\"\"$

\

$\"\"$ .

\

The two points are $\"\"$ .

\

In this case two triangles are possible.

\

\

Third vertex of the triangle is $\"\"$ or $\"\"$ .

\

Two triangles are possible.