A chord AB of the circle `x^(2)+y^(2)=a^(2)` subtends a right angle at its centre. Show that the locus of the centroid of the angle PAB as P moves on the circle is another circle.

Let AB be a chord of the circle x^2 + y^2 = r^2 Subtending a right angle at the centre, then the locus of the centroid of the triangle PAB as P moves on the circle is

Let the foci of the ellipse (x^(2))/(9) + y^(2) = 1 subtend a right angle at a point P . Then the locus of P is _

If the chord u=mx +1 of the circel x ^(2) +y^(2)=1 subtends an angle of 45^(@) at the major segment of the circle, then the value of m is-

The locus of the midpoints of chords of the circle x^(2) + y^(2) = 1 which subtends a right angle at the origin is

If the arc of a circle of radius 60 cm subtends and angle 2/3 radian at its centre , then the length of the arc will be

The common chord of the circles x^(2)+y^(2)-4x-4y=0and2x^(2)+2y^(2)=32 subtends at the origin an angle equal to

A line through (0,0) cuts the circel x ^(2) +y^(2) -2ax =0 at A and B , then the locus of the centre of the circle drawn on AB as diameter is-

Let A B be chord of contact of the point (5,-5) w.r.t the circle x^2+y^2=5 . Then find the locus of the orthocentre of the triangle P A B , where P is any point moving on the circle.

From a point on the circle x^2+y^2=a^2 , two tangents are drawn to the circle x^2+y^2=b^2(a > b) . If the chord of contact touches a variable circle passing through origin, show that the locus of the center of the variable circle is always a parabola.