Prove that the radius of a circle is perpendicular to the tangent at the point of contact.

In the adjoining figure, the sum of radii of two concentric circles is 16 cm. The length of chord AB which touches the inner circle at P is 16 cm. The difference of the radii of the given circles is

MCQ (Single)Theorem on Tangent Perpendicular to Radius at Point of ContactLength of Tangent from External Point

In the adjoining figure, XY and X'Y' are parallel tangents to a circle with centre O. Another tangent AB touches the circle at C intersecting XY at A and X'Y' at B. Prove that AB subtends right angle at the centre of the circle; or ∠AOB = 90°.

TextTheorem on Tangent Perpendicular to Radius at Point of ContactTheorem on Equal Length of Tangents from External Point

Assertion (A) : Tangents drawn at the end points of a diameter of a circle are always parallel to each other. Reason (R) : The lengths of tangents drawn to a circle from a point outside the circle are always equal.

Assertion-ReasonTheorem on Tangent Perpendicular to Radius at Point of ContactTheorem on Equal Length of Tangents from External Point

Prove that the tangents drawn at the ends of a diameter of a circle are parallel.

TextDefinition of Tangent to a CircleTheorem on Tangent Perpendicular to Radius at Point of Contact