What is the longest chord?.

Transcription

1 Section: 7-6 Topic: ircles and rcs Standard: 7 & 21 ircle Naming a ircle Name: lass: Geometry 1 Period: Date: In a plane, a circle is equidistant from a given point called the. circle is named by its. The circle below is. D E Radius Diameter radius is a segment that has one endpoint and the other endpoint. In the circle above is a radius. There are ways to draw a radius in a circle. diameter is a segment that contains and has both endpoints on the circle. In the circle above is a diameter. hord segment whose endpoints are. The is a special type of chord that goes through the center. In the circle above and are chords. What is the longest chord?. Secant that intersects a circle at is a secant. In the circle above is a secant. ll secants contain. Tangent to a circle is a in the plane of the circle that touches the circle at exactly. The point where a circle and a tangent intersect is the. 1

2 oncentric circles oncentric circles are two or more circles that lie in the same and have the same. Draw a picture of 3 concentric circles around point F. F entral ngle central angle is an angle whose is at the of a circle. P D rc Types of rcs n arc is a part of a circle. Semicircle Minor rc Major rc Description Example from above How do you know if someone is referring to a major arc or a minor arc? 2

3 rc measure ll arcs are measured in. The measure of a is the measure of its corresponding. Examples ircumference The circumference of a circle is. How can you calculate the circumference of a circle? Pi The number pi ( ) is the ratio of the to its.. Example Find the circumference of the circle r = 5in D=12ft n r = 1m Exact answer (leave π) pproximate answer (use π 3.14) 3

4 7. circle has a circumference of 48π inches. What is the radius of the circle? The diameter? nswering in terms of Pi nswering in terms of Pi, means to the symbol in your answer. (in other words give an exact answer) rc length n arc length is. To find an arc length you must write and solve a. How can you calculate arc length? Example Find the length of arc (arc = ) d=10 r=3 r= Summary/Reflection: What is the difference between the measure of an arc and the length of an arc? 4

5 Section: 11-1 Topic: Tangent Lines Standard: 21 Tangent Lines Name: lass: Geometry 1 Period: Date: to a circle is a line in the plane of the circle that intersects the circle in. The point where a circle and a tangent intersect is the.? The term tangent is derived from the Latin verb tangere, which means. ngle formed by a tangent and a radius. If a line is tangent to a circle, then the line is to the radius drawn to the point of tangency. Draw a diagram to illustrate this theorem. Finding ngle Measures Use this theorem to solve these problems involving tangents to circles. = x 120 x m<= Summary/Reflection: How is the central angle (x) related to the outside angle (y) formed by 2 tangent lines? x y 5

6 Section: 11-3 Topic: Inscribed ngles Standard: 21 Inscribed ngle Intercepted rc Name: lass: Geometry 1 Period: Date: n inscribed angle is one whose is on the circle and the sides of the angle are. The arc that connects the of an. 1) Inscribe an angle in this circle. 2) Label the points with nonrepeating letters from your name. 3) Highlight the intercepted arc. 4) Label both features. 1)Pick a point on the circle and use a straightedge to draw an inscribed angle with as the intercepted arc. 2)Label it angle 1. 3)Trace central angle patty paper. X onto 4) Fold the patty paper such that the angle is bisected. 5) Draw in the bisector you just folded. 6) ompare the bisected angle on your patty paper to 1. What is the relationship between mx and m 1? X Draw a second inscribed angle intercepting the same arc. Label it angle 2. ompare it to the angle on the patty paper. What is the relationship between m 1 and m 2? 6

7 Inscribed ngle Theorem The measure of an inscribed angle is the measure of its intercepted arc. m If arc is 70 then. If two angles intercept the same arc, how are those angles related? ngle inscribed in a semicircle. Use a straightedge and draw any inscribed angle that intercepts the arc. Label your angle 3. Estimate the measure of the inscribed angle using a corner. ompare your result to that of your neighbors. What type of special line segment is? What is the measure of arc? What type of special arc is arc? What is the measure of 3? What do all angles inscribed in semicircles have in common? 7

8 Find the missing variables: x 7 y z 120 Quadrilateral inscribed in a circle Find the values of v, w, x, y, and z. v w How are the opposite angles of the inscribed quadrilateral related? 8

9 The ngle formed by a Tangent and a hord The measure of an angle formed by a tangent and a chord is the measure of the intercepted arc. D E me me P J 140 K M S Find m<pqr Q R L Find m<lmn N Summary/Reflection: Inscribe parallelogram D in a circle below. What is a more precise name for D? What other type of parallelogram is possible? Draw and label it in the other circle. Inscribe and classify a trapezoid in the last circle. 9

10 Section: 11-4 Topic: ngles formed by chords, secants and tangents Standard: 21 Intersections a. Name: lass: Geometry 1 Period: Date: In the circle below label chord and secant D. ngles formed by intersecting and/or. m1 1 y Examples

11 Intersections a. Using a straight edge Draw secants and D intersecting outside the circle to form acute angle 1. m1 The measure of an angle formed by two secant lines that intersect outside a circle: y D Using a straight edge Draw secant and a tangent line with as the point of tangency intersecting outside the circle to form acute angle 1. m1 The measure of an angle formed by a secant line and a tangent that intersect outside a circle: y Using a straight edge Draw two tangent lines with and as the points of tangency intersecting outside the circle to form acute angle 1. m1 The measure of an angle formed by two tangent lines that intersect outside a circle: y onsider the relationship between the measures of the two arcs in this last one. an we write another formula? m1 m1 11

12 How can I remember all these formulas: For angles inside a circle: Often times are useful for stimulating memory. and are examples of this. If you are the middle of something, you have yourself to the situation. For angles outside a circle: If you yourself from the situation and are outside of it, you have yourself from it. Examples: Find the measure of the indicated angle or arc in each problem:

13 y Summary/Reflection: Illustrate how to find angle measures when the vertex is Inside the circle On the circle Outside the circle 13