What is an right angled Isosceles triangle?

The ratio between the circumradius and invadius of a right angled isosceles triangle is

Check whether the points (3 , 0) , (6 , 4) and ( - 1 , 3) are the vertices of a right -angled isosceles triangle or not. Also find the area of the triangle .

I : The points (2, -2), (-1, 2), (3, 5) are the vertices of a right angled isoceles triangle. II : The points (2, -4), (4, -2), (7, 1) form an isosceles triangle.

Show that the points (2, 3, 5), (-1, 5, -1) and (4, -3, 2) form a right angled isosceles triangle.

Show that the points (-2,5),(3,-4),(7,10) form a right angled isosceles triangle.

If (2, 4), (4, 2) are extremities of the hypotenuse of a right angled isosceles triangle, then the third vertex is

The hypotenuse of a right angled isosceles triangle has its ends at the points (1,3) and (-4,1) . Find the equations of the legs of the triangle.

Show that the point A(-4, 9, 6), B(-1,6,6), C(0,7,10) form a right angled isosceles triangle.

Show that the lines x-7y-22=0, 3x+4y+9=0 and 7x+y-54=0 form a right angled isosceles triangle.