10.3 – Apply Properties of Chords

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

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

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

In the same circle, or in congruent circles, two chords are congruent iff they are _________________ from the _____________. equidistant center and 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 4 = = 90° Congruent chords

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

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

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

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

50° 50° = 100°

360 – 85 – 65 2 = = 105°

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

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

_______________________ YES or NO Reason: _______________________ it is perpendicular and bisects

_______________________ YES or NO Reason: _______________________ it doesn’t bisect

10.7 – Graphing Circles

r : ___________________________ x : ___________________________ 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: (x, y) r r : ___________________________ x : ___________________________ y: ____________________________ Radius (distance from center) Horizontal leg length of right  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:

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

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

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

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:

We use horizontal and vertical shifts to move the center of the circle and get the standard form: 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. (3, 0)

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

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

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

d) Write the equation of the circle. 4. Find the center, the radius, then graph the circle. d) Write the equation of the circle. Ctr ( , ) r = ______ 3 1 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 8x – 13 = 6x + 9 2x – 13 = 9 2x = 22 x = 11