An isosceles right angled triangle is inscribed in the circle x2+y2=r2. If the coordinates of an end of the hypotenuse are (a, b), the coordinates of the vertex are
(b, -a)
Since the hypotenuse of a right angled triangle inscribed in a circle is a diameter of the circle. If the coordinates of the end C of the hypotenuse BC are (a, b), the coordinates of B are (-a, -b). Equation of BC is yx=ba. If A is the vertex of the isosceles triangle, then OA is perpendicular to BC and the equation of AO is yx=−ab which meets the circles x2+y2=r2 at points for which
(a2b2+1)x2=r2=a2+b2 [∵(a,b) lies on x2+y2=r2]⇒x2=b2⇒x=±b⇒ y=∓a∴ Coordinates of A are (−b,a) or (b,−a).