Presentation on theme: "Date: Sec 10-1 Concept: Tangents to Circles"— Presentation transcript:
1 Date: Sec 10-1 Concept: Tangents to Circles Objective: Given a circle, identify parts and properties as measured by a s.g.
2 Circle Center Radius Diameter Chord Secant Tangent Tangent Circles Circle Activity – Draw a diagram illustrating the words listed below. Identify each word on the illustration. LOOK IN CH 10CircleCenterRadiusDiameterChordSecantTangentTangent CirclesConcentricCommon TangentInterior of a circleExterior of a circlePoint of TangencyMinor ArcMajor ArcInscribed AngleCentral Angle
3 Example: The diagram shows the layout of the streets on Mexcaltitlan Island. 1. Name 2 secants2. Name two chords3. Is the diameter of the circle greater than HC?4. If ΔLJK were drawn, one of its sides would be tangent to the circle. Which side is it?
4 Tangent Circles 2 points of intersection 1 point of intersection Draw internal/external tangentsTangent Circles2 points of intersection1 point of intersectionNo points of intersection
5 QP l P l If l is tangent to circle Q at P, then Q Thm 10-1: If a line is tangent to a circle, then it is perpendicular to the radius drawn to the point of tangency.PlQIf l is tangent to circle Q at P, thenQP l
6 Example: If BC is tangent to circle A, find the radius of the circle. Use the pyth. Thm.r2+242 = (r+16)2r2+576 = (r+16)(r+16)r2+576 = r2+16r+16r+256r2+576 = r2+32r+256A1624rBC576 = 32r + 256320 = 32r3210 = r
7 1. What is the radius of the green Example: A green on a golf course is in the shape of a circle. A golf ball is 8 feet from the edge of the green and 28 feet from a point of tangency on the green, as shown at the right. Assume that the green is flat.1. What is the radius of the green2. How far is the golf ball from the cup at the center?
8 If l QP at P, then l is tangent to circle Q Thm 10-2: in a plane, if a line is perpendicular to a radius of a circle at its endpoint on the circle, then the line is tangent to the circlePlQIf l QP at P, then l is tangent to circle Q
9 Example: Is CE tangent to circle D? 4345DEC11Use the Pyth. Thm:= 452= 20251970 ≠ 2025No, it’s not tangent
10 If SR and TS are tangent to circle P, then SR TS Thm: If 2 segments from the same exterior point are tangent to a circle, then they are congruent.RTSPIf SR and TS are tangent to circle P, then SR TS
11 Example: AB and DA are tangent to circle C. Find x. 21X2 – 4 = 21X2 = 25X=5
14 Circle: A circle is the set of all points in a plane that are equidistant from a given point called the center of the circle. A circle with center P is called “circle P” or PTangentCenterRadiusDiameterChordSecant