PowerPoint Presentation: MATHEMATICS PROJECT : 2 Made by-: Pritam Kondar Otur,Tal -: Junnar Dist-: Pune
PowerPoint Presentation: Chapter 6 Circles
Parts of a Circle: Parts of a Circle Circle – set of all points _________ from a given point called the _____ of the circle. C Symbol: equidistant center C
PowerPoint Presentation: CHORD: a segment whose ________ are on the circle endpoints
Radius: P RADIUS: distance from the _____ to a point on the circle center Radius
Diameter: Diameter P DIAMETER: distance ______ the circle through its ______ center across Also known as the longest chord.
What is the relationship between the diameter and the radius of a circle?: What is the relationship between the diameter and the radius of a circle? r = OR D = ½ D 2 r
PowerPoint Presentation: 12 32 9 6 D = ? r = ? r = ? D = ? 24 16 4.5 12
Use P to determine whether each statement is true or false.: Use P to determine whether each statement is true or false . P Q R T S
Secant Line: Secant Line A secant line intersects the circle at exactly TWO points. SECANT sounds like second
PowerPoint Presentation: TANGENT: a LINE that intersects the circle exactly ONE time
PowerPoint Presentation: Point of Tangency
PowerPoint Presentation: Name the term that best describes the line. Secant Radius Diameter Chord Tangent
Two circles can intersect…: Two circles can intersect… in two points one point or no points
No points of intersection (different center): No points of intersection (different center)
No points of intersection (same center): Concentric Circles No points of intersection (same center) Same center but different radii
1 point of intersection (Tangent Circles): 1 point of intersection (Tangent Circles) Internally Tangent Externally Tangent
2 points of intersection: 2 points of intersection
Common Tangents: Common Tangents Internal
Common Tangents: Common Tangents External
PowerPoint Presentation: INTERIOR A point is inside a circle if its distance from the center is less than the radius.
PowerPoint Presentation: EXTERIOR A point is outside a circle if its distance from the center is greater than the radius.
PowerPoint Presentation: A point is on a circle if its distance from the center is equal to the radius.
PowerPoint Presentation: If a line (segment or ray) is tangent to a circle, then it is perpendicular to the radius drawn to the point of tangency. Point of Tangency More Pythagorean Theorem type problems! Yeah!!
PowerPoint Presentation: 1. Find x 9 x A B 12 a 2 + b 2 = c 2 x = 15 9 2 + 12 2 = x 2
PowerPoint Presentation: 2. Find RQ a 2 + b 2 = c 2 8 P R 12 Q RQ = 16 12 2 + (QR) 2 = (8+12) 2 12 2 + (QR) 2 = 20 2
PowerPoint Presentation: 3. Find the radius. r 2 + 24 2 = (r + 16) 2 16 A B 24 C r = 10 r 2 + 576 = r 2 + 32r + 256 320 = 32r
PowerPoint Presentation: R S T If two segments from the same exterior point are tangent to a circle, then they are congruent. Party hat problems!
PowerPoint Presentation: R S T 4. Find x
PowerPoint Presentation: A C B 5. Find x
PowerPoint Presentation: A C E B D 6. Find x. P
PowerPoint Presentation: T S Q P N R 7. Find NP