Download Circle Chapter

Circle Chapter
Notes
Mr. Durkin
ANGLES AND SEGMENTS INVOLED IN CIRCLES
Radius – Segment from the center of a circle to the outer edge
Diameter - Segment from one side of a circle to another passing through the
center.
Chord – Segment that touches both sides of the circle.
Secant – Segment that starts on the outside of a circle and passes through the
circle touching both sides.
Tangent – Line that is outside the circle and touches it at one point.
Central Angle – Angle formed at the center of a circle by a radius or
diameter
Inscribed Angle – Angle formed on the inside of the circle with it’s vertex
on the circles edge.
ANGLES AND ARCS OF A CIRCLE
Central Angles – Equal to the arc that it intercepts
Inscribed angles – Equal to ½ the arc that it intercepts
Inscribed angle that touches both sides of a diameter must form a right
angle.
Angle formed by a tangent and a radii or diameter form a right angle
on the edge of a circle.
Two inscribed angles that intercept the same arc are congruent.
Angles formed outside the circle equal ½ the difference of the two arcs that
it intercepts
The angle can be formed by either 2 tangents, 2 secants, or a tangent
and a secant.
Angles formed inside the circle equal ½ the sum of the two arcs that it
Intercepts.
The angle is formed by 2 chords.
THE MEASURE OF SEGEMENTS THAT ARE IN A CIRCLE
If two chords intersect in a circle, the product of the segments of one chord
must equal the product of the segments of the other.
If one of the chords is a diameter and it is perpendicular to another
chord, it bisects the chord.
If 2 secants intersect outside of the circle, the product of the measure of the
one secant and the segment outside the circle is equal to the other secant and
it’s segment outside the circle.
If 2 tangents intersect outside the circle, they must be equal.
If a tangent and a secant intersect outside the circle, the tangent squared
equals the product of the secant and it’s outside segment.