10 3 Apply Properties of Chords In the

10. 3 – Apply Properties of Chords

In the same circle, or in congruent circles, minor two ______ arcs are congruent iff their corresponding _____ are chords congruent. B C then A D

If one chord is a _________ perpendicular bisector of another chord, then the first _____ chord is the _________. diameter and then is the diameter

If a ______ diameter of a circle is perpendicular bisects to a chord, then the diameter ______ the chord and its arc. and the diameter then

In the same circle, or in congruent circles, two chords are congruent iff they are _________ from the _______. equidistant center and then

1. Find the given measure of the arc or chord. Explain your reasoning. = 105° Congruent chords

1. Find the given measure of the arc or chord. Explain your reasoning. = 360 = 90° 4 Congruent chords

1. Find the given measure of the arc or chord. Explain your reasoning. = 360 – 116 = 122° 2 Congruent chords

1. Find the given measure of the arc or chord. Explain your reasoning. = 6 Congruent arcs

1. Find the given measure of the arc or chord. Explain your reasoning. = 22 Diameter bisects chord

1. Find the given measure of the arc or chord. Explain your reasoning. = 119° Diameter bisects arc 61°

50° = 100°

360 – 85 – 65 = 2 = 105°

Find the value of x. 3 x + 16 = 12 x + 7 16 = 9 x + 7 9 = 9 x 1=x

Find the value of x. 3 x – 11 = x + 9 2 x – 11 = 9 2 x = 20 x = 10

YES or NO Reason: it is perpendicular and bisects ____________

YES or NO Reason: it doesn’t bisect ____________

10. 7 – Graphing Circles

To come up with an equation of a circle, we need to express with an equation, the idea that its graph contains all the points that are equidistant from the center. If our center is at the origin, we would have a graph that looks like the following: r (x, y) Radius (distance from center) r : ______________ Horizontal leg length of right x : ______________ y: ______________ Vertical leg length of right

Using Pythagorean theorem, we know that: _______ The circle must be then, the set of all points (x, y) that satisfy this equation. For any equation of the form: ______, the graph is the circle centered at the _____with a radius of r. origin

1. Determine the radius of the circle whose equation is given: a) r=4

1. Determine the radius of the circle whose equation is given: b)

1. Determine the radius of the circle whose equation is given: c)

2. Write the equation of a circle centered at the origin, whose radius is given: a)

2. Write the equation of a circle centered at the origin, whose radius is given: b)

2. Write the equation of a circle centered at the origin, whose radius is given: c)

We use horizontal and vertical shifts to move the center of the circle and get the standard form: h k r

3. Find the center of the circle. a) (0, – 2)

3. Find the center of the circle. b) (– 1, 7)

3. Find the center of the circle. c) (3, 0)

4. Find the center, the radius, then graph the circle. a. Ctr ( 0 , 0 ) radius: r = __ 5

4. Find the center, the radius, then graph the circle. b. Ctr (– 4 , 0 ) radius: r = __ 3

4. Find the center, the radius, then graph the circle. c. Ctr ( 2 , -1 ) r = ______ 7

4. Find the center, the radius, then graph the circle. d) Write the equation of the circle. Ctr ( 3 , 1 ) r = ______ 2 (x – 3)2 + (y – 1)2 = 4

5: Write the equation of a circle with center (15, -9) and radius 4.

6: Write the equation of a circle with center (-4, 0) and radius 11.

10. 3 10. 7 667 -668 692 -695 3 -9, 12 -14 Graphing Circles Worksheet #8 8 x – 13 = 6 x + 9 2 x – 13 = 9 2 x = 22 x = 11