Transcript Document
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 I G Secant 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 Semicircle A semicircle is an arc of a circle whose endpoints are the endpoints of the diameter. C ● A ACB is a semicircle B 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. C ● P B Two letters are required to name a minor arc: the endpoints. PC or CB are minor arcs Major Arc An arc of a circle that is larger than a semicircle. C ● A B ABC or CAB are major arcs Inscribed Angle 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 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. 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. A The m<AQB =m<APB both intercept arc AB. B Q P m<QAP = m<PBQ Both angles intercept QP Every angle inscribed in a semicircle is an right angle. Example C Each of the three angles inscribed in the semicircle is a right angle. 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 The measure of angle D + angle B=180 The measure of angle C+angle A=180 B 65 A 70 115 D 110 C 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= C= Answer C=2 pi r C=d pi Area of a circle A=? Answer A=radius square times pi The End Core-Plus Mathematics Project Home Math Department Home SAHS Home