# Draw and label on a circle:

## Presentation on theme: "Draw and label on a circle:"— Presentation transcript:

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 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
Angles in the same segment are equal.

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
Proof The angle subtended by an arc at the centre of a circle is twice the angle subtended at the circumference.

b b 2a + 2b = 2(a + b) b 180 – 2a a a

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

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

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

a a 2a

Proof The sum of the opposite angles of a cyclic quadrilateral is 180o.

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

Circle Theorem 5: Alternate Segment
Proof 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) 2a 180 – a 90 - a a

1 2 3 4 5 Double Angle Semicircle Segment Angles Cyclic Quadrilateral
Alternate Segment