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FAQs on Circles

Definition of circle

Theorem: A tangent to a circle is perpendicular to the radius through the point of contact.

Theorem:A line drawn through the end point of a radius and perpendicular to it is a tangent to the circle.

Position of point and Find the no of tangents

Theorem: The length of two tangents drawn from an external point to a circle are equal.

Theorem:If two tangents are drawn to a circle from an external point ; then (i) they subtend equal angles at the centre. (ii) they are equally inclined to the line segments ; joining the centre to that point.

Type I: A point P is 13cm from the center of the circle. The length of the tangent drawn from P to the circle is 12 cm . Find the radius of the circle ?

A circle is touching the side BC of `DeltaABC` at P and touching AB and AC produced at Q and R respectively Prove that `AQ=1/2`(Perimeter of `DeltaABC`)

Type III: Two concentric circles of radii 5cm and 3cm . Find the length of the chord of the larger circle which touches the smaller circle.

Type IV: A circle touches the sides of the quadrilateral ABCD at P, Q, R, and S respectively. Show that the angles subtended at the center by a pair of opposite sides are supplementary.

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