Show that , The tangent at any point of a circle is perpendicular to the radius through the point of contact.

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

The perpendicular from the origin to the tangent at any point on a curve is equal to the abscissa of the point of contact. Also curve passes through the point (1,1). Then the length of intercept of the curve on the x-axis is__________

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

Find the equation of the curve whose length of the tangent at any point on ot, intercepted between the coordinate axes is bisected by the point of contact.

Choose the correct answer and give justification for each. (i) The angle between a tangent to a circle and the radius at the point of contact is

A tangent is drawn to each of the circles x^2+y^2=a^2 and x^2+y^2=b^2dot Show that if the two tangents are mutually perpendicular, the locus of their point of intersection is a circle concentric with the given circles.

Show that the tangent at any point on an ellipse and the tangent at the corresponding point on its auxiliary circle intersect on the major axis.

Fill in the blanks A tangent PQ at a point P of a circle of radius 5cm meets a line through the centre O at a point Q so that OQ=13cm . Find length of PQ.

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

From a variable point on the tangent at the vertex of a parabola y^2=4a x , a perpendicular is drawn to its chord of contact. Show that these variable perpendicular lines pass through a fixed point on the axis of the parabola.