Find the equation of the circle in which the chord joining the points `(a,b) and (b, - a)` subtends an angle of `45^@` at any point on the circumference of the circle.

Find the equation of the circle if the chord of the circle joining (1, 2) and (-3,1) subtents 90^0 at the center of the circle.

The locus of the mid-points of the chords of the circle of lines radiùs r which subtend an angle pi/4 at any point on the circumference of the circle is a concentric circle with radius equal to (a) (r)/(2) (b) (2r)/(3) (c) (r )/(sqrt(2)) (d) (r )/(sqrt(3))

Find the equations of the chords of the parabola y^2= 4ax which pass through the point (- 6a, 0) and which subtends an angle of 45^0 at the vertex.

Find the locus of a point P If the join of the points (2,3) and (-1,5) subtends a right angle at P.

chord AB of the circle x^2+y^2=100 passes through the point (7,1) and subtends are angle of 60^@ at the circumference of the circle. if m_1 and m_2 are slopes of two such chords then the value of m_1*m_2 is

Find the locus of a point, so that the join of points (-5, 1) and (3, 2) subtends a right angle at the moving point.

Find the locus of the mid-point of the chords of the circle x^2 + y^2 + 2gx+2fy+c=0 which subtend an angle of 120^0 at the centre of the circle.

Find the equation to the circle, of radius a, which passes through the two points on the axis of x which are at a distance b from the origin.

A chord of a circle of radius 12 cm subtends an angle of 120^@ at the centre. Find the area of the corresponding segment of the circle.

Find the length of the chord which subtends an angle of 120^(@) at the centre of the circle of radius 6 cm.