Draw and label on a circle Centre Radius

Draw and label on a circle: Centre Radius Diameter Circumference Chord Tangent Arc Sector (major/minor) Segment (major/minor) Science grinds

Circle Fact 1. Isosceles Triangle Any triangle AOB with A & B on the circumference and O at the centre of a circle is isosceles. r a 180 - 2 a r Science grinds a

Circle Fact 2. Tangent and Radius The tangent to a circle is perpendicular to the radius at the point of contact. Science grinds

Circle Fact 3. Two Tangents The triangle produced by two crossing tangents is isosceles. Science grinds

Circle Fact 4. 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. Science grinds

Circle Theorem 1: Double Angle The angle subtended by an arc at the centre of a circle is twice the angle subtended at the circumference. Science grinds

Circle Theorem 2: Semicircle The angle in a semicircle is a right angle. Science grinds

Circle Theorem 3: Segment Angles in the same segment are equal. Science grinds

Circle Theorem 4: Cyclic Quadrilateral The sum of the opposite angles of a cyclic quadrilateral is 180 o. Science grinds

Circle Theorem 5: Alternate Segment The angle between a chord and the tangent at the point of contact is equal to the angle in the alternate segment. Science grinds

Circle Theorem 1: Double Angle The angle subtended by an arc at the centre of a circle is twice the angle subtended at the circumference. Science grinds

b 180 - 2 b 2 a + 2 b = 2(a + b) b a 180 – 2 a a Science grinds

Circle Theorem 2: Semicircle The angle in a semicircle is a right angle. Science grinds

b 360 – 2(a + b) = 180 = 2(a + b) 180 – 2 b 90 = (a + b) 180 – 2 a b a a Science grinds

Circle Theorem 3: Segment Angles in the same segment are equal. Science grinds

a a 2 a Science grinds

Circle Theorem 4: Cyclic Quadrilateral The sum of the opposite angles of a cyclic quadrilateral is 180 o. Science grinds

a 2 a + 2 b = 360 2(a + b) = 360 2 b a + b = 180 2 a b Science grinds

Circle Theorem 5: Alternate Segment The angle between a chord and the tangent at the point of contact is equal to the angle in the alternate segment. Science grinds

90 - a a 180 – 2(90 – a) 180 – 180 + 2 a 2 a 90 - a a Science grinds

Double Angle Segment Angles Semicircle Cyclic Quadrilateral Science grinds Alternate Segment