Circles Vocabulary And Properties Vocabulary And Properties Core-Plus Mathematics Project Home Math Department Home SAHS Home

Circle A set of all points in a plane at a given distance from a given point in the plane..

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

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 Is a segment whose endpoints lie on the circle. A B D C

Diameter A chord passing through the center of a circle. I J

Secant A line that contains a chord.

Tangent A line in the plane of the circle that intersects the circle in exactly one point.

Semicircle A semicircle is an arc of a circle whose endpoints are the endpoints of the diameter. Is a semicircle

Minor Arc An arc of a circle that is smaller than a semicircle. The minor arc is AP (clockwise) or PD (clockwise). A D P

Major Arc An arc of a circle that is larger than a semicircle. The major arc would be PA (clockwise) or DP (counter clockwise). AD P

Inscribed Angle An angle whose vertex lies on a circle and whose sides contain chords of a circle. B A C D

Central Angle An angle whose vertex is the center of the circle. A O B

Properties of Circles The measure of a central angle is two times the measure of the angle that subtends the same arc.

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

Property #2 Angles inscribed in the same arc are congruent.

Example The m<AQB and the m<APB are congruent because they both inscribe arc AB. The m<QAP and m<QBP would be congruent because they inscribe arc QP. A Q B P

Property #3 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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