Circles Vocabulary And Properties Vocabulary And Properties

Circle A set of all points in a plane at a given distance (radius) from a given point (center) in the plane.  r center

Radius A segment from a point on the circle to the center of the circle.  r

Congruent Circles Two circles whose radii have the same measure. r =3 cm

Concentric Circles Two or more circles that share the same center.. 

Chord A segment whose endpoints lie on the circle. Segments AB & CD are chords of G A segment whose endpoints lie on the circle. Segments AB & CD are chords of G A B D C  G

Diameter A chord passing through the center of a circle. Segment IJ is a diameter of G A chord passing through the center of a circle. Segment IJ is a diameter of G I J  G

Secant A line that passes through two points of the circle. A line that contains a chord. A line that passes through two points of the circle. A line that contains a chord.

Tangent A line in the plane of the circle that intersects the circle in exactly one point.  ● ● The point of contact is called the Point of Tangency The point of contact is called the Point of Tangency

Semicircle A semicircle is an arc of a circle whose endpoints are the endpoints of the diameter. is a semicircle  C B A ● Three letters are required to name a semicircle: the endpoints and one point it passes through.

Minor Arc An arc of a circle that is smaller than a semicircle. P  C B ● PC or CB are minor arcs Two letters are required to name a minor arc: the endpoints.

Major Arc An arc of a circle that is larger than a semicircle.  C B A ● ABC or CAB are major arcs

Inscribed Angle An angle whose vertex lies on a circle and whose sides contain chords of a circle. B A C D <ABC & <BCD are inscribed angles

Central Angle An angle whose vertex is the center of the circle and sides are radii of the circle. A K B  <AKB is a central angle

Properties of Circles The measure of a central angle is two times the measure of the inscribed angle that intercepts the same arc. P A B C m <APB = 2 times m <ACB ½ m <APB = m <ACB x 2x

Example If the m <C is 55 , then the m <O is 110 . Both angle C and angle O intercept the same arc, AB. O A B C 55° 110°

Angles inscribed in the same arc are congruent. A Q B P m <QAP = m <PBQ Both angles intercept QP The m <AQB = m <APB both intercept arc AB.

Every angle inscribed in a semicircle is an right angle.

Example Each of the three angles inscribed in the semicircle is a right angle. A B C D E Angle B, C, and D are all 90 degree angles.

Property #4 The opposite angles of a quadrilateral inscribed in a circle are supplementary.

Example The measure of angle D + angle B=180  The measure of angle C+angle A=180  The measure of angle D + angle B=180  The measure of angle C+angle A=180  A B C D

Property #5 Parallel lines intercept congruent arcs on a circle.

Example A B Arc AB is congruent to Arc CD C D

Formulas What are the two formulas for finding circumference? C= What are the two formulas for finding circumference? C=

Answer C=2 pi r C=d pi C=2 pi r C=d pi

Area of a circle A=?

Answer A=radius square times pi

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