Date: Sec 10-1 Concept: Tangents to Circles Objective: Given a circle, identify parts and properties as measured by a s.g.

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 10 Circle Center Radius Diameter Chord Secant Tangent Tangent Circles Concentric Common Tangent Interior of a circle Exterior of a circle Point of Tangency Minor Arc Major Arc Inscribed Angle Central Angle

Example: The diagram shows the layout of the streets on Mexcaltitlan Island. 1. Name 2 secants 2. Name two chords 3. 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?

Tangent Circles 2 points of intersection 1 point of intersection Draw internal/external tangents Tangent Circles 2 points of intersection 1 point of intersection No points of intersection

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. P l Q If l is tangent to circle Q at P, then QP  l

Example: If BC is tangent to circle A, find the radius of the circle. Use the pyth. Thm. r2+242 = (r+16)2 r2+576 = (r+16)(r+16) r2+576 = r2+16r+16r+256 r2+576 = r2+32r+256 A 16 24 r B C 576 = 32r + 256 -256 -256 320 = 32r 32 10 = r

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 green 2. How far is the golf ball from the cup at the center?

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 circle P l Q If l  QP at P, then l is tangent to circle Q

Example: Is CE tangent to circle D? 43 45 D E C 11 Use the Pyth. Thm: 112+432 = 452 121+1849 = 2025 1970 ≠ 2025 No, it’s not tangent

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. R T S P If SR and TS are tangent to circle P, then SR  TS

Example: AB and DA are tangent to circle C. Find x. 21 X2 – 4 = 21 + 4 +4 X2 = 25 X=5

Statements Reasons 1. 2. 3. 4. 5. Seg. Addition Post. 6. 1. 2. PQTQ; QSQR PQ=TQ; QS=QR 4. PQ+QS = TQ+QR 5. 6.

Today’s Work In Class: HW:

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 P Tangent Center Radius Diameter Chord Secant