11 1 circles lesson
- 1. Parts of a CircleParts of a Circle You will learn to identify and use parts of circles. 1) circle 2) center 3) radius 4) chord 5) diameter 6) concentric
- 2. Parts of a CircleParts of a Circle A circle is a special type of geometric figure. All points on a circle are the same distance from a ___________.center point O B A The measure of OA and OB are the same; that is, OA OB
- 3. Parts of a CircleParts of a Circle Definition of a Circle A circle is the set of all points in a plane that are a given distance from a given _____ in the plane, called the ______ of the circle. point center P Note: a circle is named by its center. The circle above is named circle P.
- 4. Parts of a CircleParts of a Circle There are three kinds of segments related to circles. A ______ is a segment whose endpoints are the center of the circle and a point on the circle. radius A _____ is a segment whose endpoints are on the circle.chord A ________ is a chord that contains the centerdiameter
- 5. Parts of a CircleParts of a Circle Segments of Circles K A diameterchordradius R K J K T G KA is a radius of K JR is a chord of K GT is a diameter of K From the figures, you can not that the diameter is a special type of _____ that passes through the center. chord
- 6. Parts of a CircleParts of a Circle C A D B Q AD is a diameter of Q . Use Q to determine whether each statement is true or false. False; Segment AD does not go through the center Q. AC is a chord of Q . True; AD is a radius of Q . False;
- 7. Theorem 11-1 Theorem 11-2 Parts of a CircleParts of a Circle All radii of a circle are _________.congruent P R S T G PR≃PG≃PS≃PT The measure of the diameter d of a circle is twice the measure of the radius r of the circle. d = 2r or 1 2 d= r
- 8. Parts of a CircleParts of a Circle C A B Q 3x-5 17 Find the value of x in Q. 3x – 5 = 2(17) 3x – 5 = 34 3x = 39 x = 13
- 9. Parts of a CircleParts of a Circle If QR = 1, find RT RT = TQ – QR RP Q T BA P has a radius of 5 units, and T has a radius of 3 units. RT = 3 – 1 RT = 2 If QR = 1, find PQ PQ = PR – QR PQ = 5 – 1 PQ = 4 If QR = 1, find AB AB = 2(AP) + 2(BT) – 1 AB = 2(5) + 2(3) – 1 AB = 10 + 6 – 1 AB = 15
- 10. Parts of a CircleParts of a Circle If AR = 2x, find AP in terms of x. AR = 2(AP) RP Q T BA P has a radius of 5 units, and T has a radius of 3 units. 2x = 2(AP) x = AP If TB = 2x, find QB in terms of x. QB = 2(TB) QB = 2(2x) QB = 4x
- 11. S Parts of a CircleParts of a Circle Because all circles have the same shape, any two circles are similar. However, two circles are congruent if and only if (iff) their radii are _________.congruent Two circles are concentric if they meet the following three requirements: Circle R with radius RT and circle R with radius RS are concentric circles. They lie in the same plane. They have the same center. They have radii of different lengths. R T