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)
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 a
Circle Fact 2. Tangent and Radius The tangent to a circle is perpendicular to the radius at the point of contact.
Circle Fact 3. Two Tangents The triangle produced by two crossing tangents is isosceles.
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.
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.
Circle Theorem 2: Semicircle The angle in a semicircle is a right angle.
Circle Theorem 3: Segment Angles in the same segment are equal.
Circle Theorem 4: Cyclic Quadrilateral The sum of the opposite angles of a cyclic quadrilateral is 180 o.
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.
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.
b 180 - 2 b 2 a + 2 b = 2(a + b) b a 180 – 2 a a
Circle Theorem 2: Semicircle The angle in a semicircle is a right angle.
b 360 – 2(a + b) = 180 = 2(a + b) 180 – 2 b 90 = (a + b) 180 – 2 a b a a
Circle Theorem 3: Segment Angles in the same segment are equal.
a a 2 a
Circle Theorem 4: Cyclic Quadrilateral The sum of the opposite angles of a cyclic quadrilateral is 180 o.
a 2 a + 2 b = 360 2(a + b) = 360 2 b a + b = 180 2 a b
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.
90 - a a 180 – 2(90 – a) 180 – 180 + 2 a 2 a 90 - a a
Double Angle Segment Angles Semicircle Cyclic Quadrilateral Alternate Segment
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