From a fixed point `A` on the circumference of a circle of radius `r ,` the perpendicular `A Y` falls on the tangent at `Pdot` Find the maximum area of triangle `A P Ydot`

A point P is given on the circumference of a circle of radius r. The chord QR is parallel to the tangent line at P. Find the maximum area of the triangle PQR.

A point P is given on the circumference of a circle of radius r. Chord QR is parallel to the tangent at P. Determine the maximum possible area of the triangle PQR.

If a point P is 17 cm from the centre of a circle of radius 8 cm, then find the length of the tangent drawn to the circle from point P.

The circle x^2+y^2=1 cuts the x-axis at Pa n dQdot Another circle with center at Q and variable radius intersects the first circle at R above the x-axis and the line segment PQ at S. Find the maximum area of triangle QSR.

If P(t^2,2t),t in [0,2] , is an arbitrary point on the parabola y^2=4x ,Q is the foot of perpendicular from focus S on the tangent at P , then the maximum area of P Q S is (a) 1 (b) 2 (c) 5/(16) (d) 5

P is a variable on the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 with A A ' as the major axis. Find the maximum area of triangle A P A '

XY is a diameter of a circle. PAQ is a tangent to the circle at the point A lying on the circumference. The perpendicular drawn on the tangent to the circle from X intersects PAQ at Z. Prove that XA is a bisector of angle YXZ." "[GP-X]

Prove that the tangent and the radius through the point of contact of a circle are perpendicular to each other.

P is the variable point on the circle with center at C. C A and C B are perpendiculars from C on the x- and the y-axis, respectively. Show that the locus of the centroid of triangle P A B is a circle with center at the centroid of triangle C A B and radius equal to the one-third of the radius of the given circle.

If the radius of the circle is r then find the area of circle?