Write True or False
P is any point inside the circle. The tangent to the circle always passes through the point P.

P is a point inside a circel: NO tangent of the circle will pass through P.

AB is a diameter of a circle with centre O , P is any point on the circle, the tangent drawn through the point P intersects the two tangents drawn through the points A and B at the points Q and R respectively. If the radius of the circle be r , then prove that PQ.PR=r^(2) .

P ,Q , and R are the feet of the normals drawn to a parabola (y-3)^2=8(x-2) . A circle cuts the above parabola at points P ,Q ,R ,a n dS . Then this circle always passes through the point.

OA is the radius of a circle with centre at Q, AQ is its chrod and C is any point on the circle. A circle passes through the point O,A,C intesect the chrod AQ at the point P. Prove that CP=PQ

Construct a circle of radius 2.5 cm. Take any point on the circle and draw a tangent to the circle at that point.

Write True or False: Only one circle can be drawn through three collinear points.

Let , RS be the diameter of the circle x^(2) + y^(2) = 1 , where S is the point ( 1,0) . Let P be a variable point (other then R and S ) on the circle and tangents to the circle at s and P meet at the point Q . The normal to the circle at P intersects a line drawn through Q parallel to RS at point E . The locus of E passes through the point (s)

Prove that the tangent to the circle at any point on it is perpendicular to the radius passes through the point of contact.

The tangent at any point P to a curve C intersects the coordinate axes at A and B. If P be the mid-point of the line segment AB and the curve passes through the point (1,1), find the equation of the curve C.

Tangent to a curve intercepts the y-axis at a point P .A line perpendicular to this tangent through P passes through another point (1,0). The differential equation of the curve is