Vocabulary And Properties Circles 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 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  B A G D C

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

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

The point of contact is called the 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

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

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

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

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

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

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

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

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

Every angle inscribed in a semicircle is an right angle.

Example Each of the three angles inscribed in the semicircle is a right angle. C D B A 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 B 65 A 70 110 C 115 D The measure of angle D + angle B=180 The measure of angle C+angle A=180 B 65 A 70 110 C 115 D

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

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

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

Answer C=2 pi r C=d pi

Area of a circle A=?

Answer A=radius square times pi

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