1 / 9

Lesson 10-R

Lesson 10-R. Chapter 10 Review. Objectives. Review Chapter 10 material. Parts of Circles. Circumference (Perimeter) once around the outside of the circle; Formulas: C = 2 π r = d π Chord segment with endpoints of the edge of the circle Radius

zachary-carter
Télécharger la présentation

Lesson 10-R

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Lesson 10-R Chapter 10 Review

  2. Objectives • Review Chapter 10 material

  3. Parts of Circles • Circumference (Perimeter) • once around the outside of the circle; Formulas: C = 2πr = dπ • Chord • segment with endpoints of the edge of the circle • Radius • segment with one endpoint at the center and one at the edge • Diameter • segment with endpoints on the edge and passes thru the center • longest chord in a circle • is twice the length of a radius • Other parts • Center: is also the name of the circle • Secant: chord that extends beyond the edges of the circle • Tangent: a line (segment) that touches the circle at only one point

  4. Arcs in Circles • Arc is the edge of the circle between two points • An arc’s measure = measure of its central angle • All arcs (and central angles) have to sum to 360° • If two arcs have the same measure then the chords that form those arcs have the same measure • If a radius is perpendicular to a chord then it bisects the chord and the arc formed by the chord (example arc AED below) • Major Arc (example: arc DAB) • measures more than 180° • more than ½ way around the circle • Minor Arc (example: arc AED) • measures less than 180° • less than ½ way around the circle • Semi-circle (example: arc EAB) • measures 180° • defined by a diameter BE is a diameter and AB = AD 120° B A C 120° 60° E D 60°

  5. Angles Associated with Circles V K L minor arc LK = 10° minor arc NM = 70° minor arc FG = 110° minor arc EH = 36° minor arc BD = 110° B F E 10° A V M 36° N C C 110° 110° H C D G 70°

  6. Segments Inside/Outside of Circles • Segments that intersect inside or outside the circle have the length of their parts defined by: Two ChordsInside a Circle Two SecantsFrom Outside Point Secant & Tangent From Outside Point J J K 4 3 5 6 L K K L 3 4 J T 9 8 7 11 6 N N M M M LJ · JM = NJ · JK 3  8 = 6  4 JT · JT = JK · JM 6  6 = 3  12 JL · JN = JK · JM 5  12 = 4  15 Inside the circle, it’s the parts of the chordsmultiplied together Outside the circle, it’s the outside part multiplied by the whole length OW = OW

  7. Tangents and Circles • Tangents and radii always form a right angle • We can use the converse of the Pythagorean theorem to check if a segment is tangent • The distance from a point outside the circle along its two tangents to the circle is always the same distance Example 1 Given: JT is tangent to circle C JC = 25 and JT = 20 Find the radius Example 2 Given: same radius as example 1 JC = 25 and JS = 16 Is JS tangent to circle C? J S T JC² = JT² + TC² 25² = 20² + r² 625 = 400 + r² 225 = r² 15 = r JC² = JS² + SC² 25² = 16² + 15² 625 = 256 + 225 625 ≠ 481 JS is not tangent C

  8. Equation of Circles • A circle’s algebraic equation is defined by: (x – h)² + (y – k)² = r² where the point (h, k) is the location of the center of the circleand r is the radius of the circle • Circles are all points that are equidistant (that is the distance of the radius) from a central point (the center)

  9. Summary & Homework • Summary: • A • Homework: • study for the test

More Related