Circle $act 1% &sosceles Triangle Any triangle AOB with A & B on the circumference and O at the centre of a circle is isosceles.
r a 1! " #a
r
a
Circle $act #% Tangent and Radius The tangent to a circle is perpendicular to to the radius at the point of contact. contact.
Circle $act '% Two Tangents The triangle produced by two crossing tangents is isosceles.
Circle $act % Chords If a radius bisects a chord, it does so at right angles, and if a radius cuts a chord at right angles, it bisects it.
Circle Theorem 1: Double Angle Angle The angle subtended by an arc at the centre of a circle is twice the angle subtended at the circumference.
Circle Theorem #: Semicircle The angle in a semicircle is a right angle.
Circle Theorem ': Segment Angles Angles Angles in the same segment are equal.
Circle Theorem : Cclic *uadrilateral The sum of the opposite angles of a cyclic quadrilateral is 1! o.
Circle Theorem +: Alternate Alternate Segment Segment The angle between a chord and the tangent at the point of contact is equal to the angle in the alternate segment.
Circle Theorem 1: Double Angle Angle The angle subtended by an arc at the centre of a circle is twice the angle subtended at the circumference.
b
1! " #b #a - #b . #(a - b)
b a
1! , #a
a
Circle Theorem #: Semicircle The angle in a semicircle is a right angle.
b
'! , #(a - b) . 1! 1! . #(a - b) 1! , #b
0! . (a - b)
1! , #a b a a
Circle Theorem ': Segment Angles Angles Angles in the same segment are equal.
a
a
#a
Circle Theorem : Cclic *uadrilateral The sum of the opposite angles of a cyclic quadrilateral is 1! o.
a #a - #b . '! #(a - b) . '! #b
a - b . 1!
#a
b
Circle Theorem +: Alternate Alternate Segment Segment The angle between a chord and the tangent at the point of contact is equal to the angle in the alternate segment.
