draw and label on a circle: centre radius diameter circumference chord tangent arc
DESCRIPTION
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 - 2a. r. a. - PowerPoint PPT PresentationTRANSCRIPT
Draw and label on a circle:
Centre
Radius
Diameter
Circumference
Chord
Tangent
Arc
Sector (major/minor)
Segment (major/minor)
a
a
180 - 2a
r
r
Circle Fact 1. Isosceles Triangle
Any triangle AOB with A & B on the circumference and O at the centre of a circle is isosceles.
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
Angles in the same segment are equal.
Circle Theorem 4: Cyclic Quadrilateral
The sum of the opposite angles of a cyclic quadrilateral is 180o.
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.
a
ab
b
180 - 2b
180 – 2a
2a + 2b
= 2(a + b)
Circle Theorem 2: Semicircle
The angle in a semicircle is a right angle.
180 – 2a
180 – 2b
a
a
b
b
360 – 2(a + b) = 180
180 = 2(a + b)
90 = (a + b)
Circle Theorem 3: Segment Angles
Angles in the same segment are equal.
a
a
2a
Circle Theorem 4: Cyclic Quadrilateral
The sum of the opposite angles of a cyclic quadrilateral is 180o.
a
b
2a
2b
2a + 2b = 360
2(a + b) = 360
a + b = 180
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.
a
90 - a
90 - a
180 – 2(90 – a)
180 – 180 + 2a 2a
a
Double Angle Semicircle
Segment Angles Cyclic Quadrilateral Alternate Segment