CIRCLES AND TANGENTS PREPARED BY MS SARVATH PARTS

CIRCLES AND TANGENTS PREPARED BY : MS. SARVATH.

PARTS OF A CIRCLE.

Circle Theorem 1 v Angles standing on the same arc of a circle and in the same segment are equal.

Circle Theorem 2 v The angle which the arc of a circle subtends at the centre is equal to twice the angle it subtends at any point on the remaining circumference.

Circle Theorem 3 v The opposite angles of a cyclic quadrilateral are supplementary.

Circle Theorem 4 v Any exterior angle of a cyclic quadrilateral is equal to the opposite interior angle.

Circle Theorem 5 v The angle in a semicircle is a right angle.

TANGENT PROPERTIES OF A CIRCLE A tangent is a line which just touches a circle at one point only. This point is called point of tangency.

Tangent Property 1 v A tangent to a circle is perpendicular to the radius drawn from the point of contact.

Tangent Property 2 v The two tangents drawn from an external point to a circle are the same length.

Tangent Property 2. 1 The equal tangents from a point outside also make equal angles with the chord joining the points of tangency.

Tangent Property 2. 2 The line drawn from the point where the tangents meet to the centre of the circle bisects the angle between the two tangents.

Tangent Property 2. 3

Tangent Property 2. 4 If two circles touch internally or externally then the line which passes through their centres, also passes through the point of tangency.

Tangent Property 3 v The angle between a tangent and a chord drawn from the point of contact is equal to any angle in the alternate segment.

CHORDS A chord is a straight line which joins two points on the circumference of a circle. A diameter is a chord drawn through the centre of a circle. If a diameter of a circle is at right angles to a chord then it divides the chord into two equal parts.

Chord Theorem Chords which are equal in length are equidistant from the centre of the circle. The converse is also true, i. e. , chords which are equidistant from the centre of the circle are equal in length.

Intersecting Chords Theorem

SECANT A line which cuts a circle at two points is called a secant.

Intersecting Secants Theorem

Secant-Tangent Theorem