## Prove and apply angle and chord properties of circles (VCMMG366)

LO: To prove and apply angle and chord properties of circles

Know:

• The properties of a circle
• Vocabulary of a circle, such as arc, centre, circumference, radius, diameter, chord, sector and segment.

Understand:

• That circles have certain angular properties.

Do:

• I can prove and apply angle and chord properities in circles.

# Angle Properties in Circles ## The inscribed angle is always half the size of the central angle. ### An angle inscribed in a semicircle is always a right angle. ### Angles in the same segment (same 2 starting points on the circumference) are always equal. ### Opposite angles in a cyclic quadrilateral add up to 180 degrees or is supplementary. # Chord Properties in Circles ### A chord is a straight line from one point on the circumference of a circle to another. ### It also forms a 90 degree angle between the chord and the radius. ### Chords that are equal in length are equidistant (same distance) from the circle centre. # Tangent and Secants ### A tangent is a line that touches the circumference of a circle at one point only. ### A tangent that touches a radius of the circle always creates a 90 degree angle (right angle). ### If two tangents intersect outside of a circle, the distances along the tangent from the intersection to the circumference of the circle are equal. ### If two secants intersect outside a circle, the product of the entire secant length by the external secant length will be the same. 