Name Chapter 12: Circles
Chapter 12 Calendar Sun Mon Tue Wed Thu Fri Sat May 13 12.1 (Friday) 14 Chapter 10/11 Assessment 15 12.2 12.1 11W Due 16 12.3 12.2 HW Due 17 12.1-123 Review 12.3 HW Due 18 12.1-123 Review 19 /0 21 12.1-12.3 Review 22 12.1-123 Quiz 23 12.4 24 12.3 & 12.4 Practice 25 12.5 26 12.4 HW Due 27 28 Memorial Day-No School _.4 29 Completing the Square 12.5 HW Due 30 Chapter 12 Practice Test Completing the Square HW Due 31 Chapter 12 Review 3 4 5 6 7 Final Review June 1 Chapter 12 Test 8 Final Review 2 9 10 11 Final Review 12 Final Review FERP Due 13 1st & 2nd Hour Flnals 14 3rd & 4th Hour Finab 15 5th Hour Finals 16
12.1 Tangent Lines Warm-up: I can... Identify tangent lines Use the right triangles that result from tangent lines to find missing lengths Homework: 12.1 Page 665 #1-4, 7-9, 11-14, 17, 22 i A tangent to a circle is a line in the plane that intersects the circle in exactly one point. The point of tangency is the point where a circle and a tangent intersect. A 2 1
Theorem 12.1-If a line is tangent to a circle, then the line is perpendicular to the radius drawn to the point of tangency. BA is tangent to circle C at point A. Find the value of x. 2
A belt fits tightly around two circular pulleys, as shown. Find the distance between the centers of the pulleys. Theorem 12.2-If a line in the plane of a circle is perpendicular to the radius at its endpoint on the circle, then the line is tangent to the circle.?4, 1 le ) 6 3
Determine if a tangent line is shown in the diagram. In the picture below, the dashed (blue) circle is inscribed inside the triangle. The solid (red) circle is circumscribed around the triangle. ( What do you notice about the triangle if it circumscribed about a circle? Or, the triangle is circumscribed around the blue circle. 8 4
Theorem 12.3-Two segments tangent to a circle from a point outside the circle are congruent. Circle C is inscribed in quadrilateral XYZW. Find the perimeter of this quadrilateral. 5
I can... -Identify tangent lines -Use the right triangles that result from tangent lines to find missing lengths Homework: 12.1 Page 665 #1-4, 7-9, 11-14, 17, 22 11 12.2 Chords and Arcs Warm-up: I can... Use congruent chords, arcs, and central angles -Recognize properties of lines through the center of a circle Homework: 12.2 Page 673 #1, 3-8, 10-19, 26, 42-46, 49, 50 12 6
A chord is a segment whose endpoints are on a circle. Theorem 12.4-Within a circle or in congruent circles: 1. Congruent central angles have congruent chords 2. Congruent chords have congruent arcs 3. Congruent arcs have congruent central angles 14 7
In the diagram, radius OX bisectszam. What can you conclude? Remind me... how do we describe the distance from a point to a line? 16 8
Theorem 12.5-Within a circle or in congruent circles: 1. Chords equidistant from the center are congruent 2. Congruent chords are equidistant from the center 17 9
Theorem 12.6-In a circle, a diameter that is perpendicular to a chord bisects the chord and its arcs Theorem 12.7-In a circle, a diameter that bisects a chord (that is not a diameter) is perpendicular to the chord Theorem 12.8-In a circle, the perpendicular bisector of a chord contains the center of the circle 19 P and Q are points on circle 0. The distance from 0 topq is 15 inches and PQ=16 in. Find the length of the radius. 20 10
Find the distance from the center of a circle to a chord 30 m long if the diameter of the circle is 34 m. 21 Two circles intersect and have a common chord 24 cm long. The centers of the circles are 21 cm apart, a length which is perpendicular to the common chord. The radius of one circle is 13 cm. Find the radius of the other circle. 22 11
Two concentric circles have radii 3 and 7. Find, to the nearest hundredth, the length of a chord of the larger circle that is tangent to the smaller circle. 23 I can.... Use congruent chords, arcs, and central angles ' Recognize properties of lines through the center of a circle Homework: 12.2 Page 673 #1, 3-8, 10-19, 26, 42-46, 49, 50 24 12
12.3 Inscribed Angles Warm-up: I can....find the measure of an inscribed angle.find the measure of an angle formed by a tangent and a chord Homework: 12.3 Page 681 #5-22 25 Inscribed angle-an angle is inscribed in a circle if the vertex of the angle is on the circle and the sides of the angle are chords of the circle. 26 13
Inscribed Angle Theorem-The measure of an inscribed angle is half the measure of its intercepted arc. 1 m/ B = nia 2 27 14
Corollaries to the Inscribed Angle Theorem 1. Two inscribed angles that intercept the same arc are congruent. 2. An angle inscribed in a semicircle is a right angle. 3. The opposite angles of a quadrilateral inscribed in a circle are supplementary. 29 Find the values of the missing variables. 15
Theorem 12.10-The measure of an angle formed by a tangent and a chord is half the measure of the intercepted arc. irizc = 2 31 Find the measure of the variables and angles. 16
I can....find the measure of an inscribed angle.find the measure of an angle formed by a tangent and a chord Homework: 12.3 Page 681 #5-22 33 12.4 Angle Measures and Segment Lengths Warm-up: Do the problem on the next slide. I can....find the measures of angles formed by chords, secants, and tangents.find the lengths of segments associated with circles Homework: 12.4 Page 691 #1-15, 20-24, 43-47 34 17
In the diagram,fe andfp are tangents to circle C. Find each arc measure, angle measure, or length. 2. mra = 3. Trig0 4. ntlead = 5. mlaec = 6. CE= 7, OF = 8. CF = 9. rnzefd = 35 Secant-a line that intersects a circle at two points Theorem 12.11-The measure of an angle formed by two lines that: 1. Intersect inside a circle is half the sum of the measures of the intercepted arcs. inz1= 1 (x+ y) Y 2 2. Intersect outside a circle is half the difference of the measures of the intercepted arcs. 1 x y) 2 36 18
Theorem 12.12-For a given point and circle, the product of the lengths of the two segments from the point to the circle is constant along any line through the point and circle. a b=c d (y + z)y t2 38 19
A tram travels from point A to point B along the arc of a circle with radius of 125 feet. Find the shortest distance from point A to point B. 40 20
I can... 'Find the measures of angles formed by chords, secants, and tangents "Find the lengths of segments associated with circles Homework: 12.4 Page 691 #1-15, 20-24, 43-47 41 12.5 Circles in the Coordinate Plane Warm-up: I can... "Write an equation for a circle -Find the center and radius of a circle Homework: 12.5 Page 697 #3-21 (every 3), 27-39 odd, 45, 46 42 21
Remember, a circle is a set of all points equidistant from a given point, called the center. 43 How would you describe this circle? 22
So how can we describe a circle in general? Write the standard equation of a circle with center (-8, 0) and radius j5. 46 23
Write the equation of a circle with center (5, 8) that passes through the point (-15, -13). 47 Write the equation of a circle whose diameter's endpoints are (-1, 0) and (-5, -3). 48 24
Find the center and radius of the circle I can... Write an equation for a circle 'Find the center and radius of a circle Homework: 12.5 Page 697 #3-21 (every 3), 27-39 odd, 45, 46 50 25
Completing the Square 1. Expand the following perfect square binomials. a. (x + 2)2 b. (x + 3)2 c. (x + 4)2 What pattern do you see? 2. Using the pattern, decide whether each of the following are perfect square trinomials (yes or no). a. x2 + 2x + 1 b. x2 8x + 16 c. x2 + 4x+ 8 d. x2 + 3x + CO e. x2 10x + 25 f. x2 + Sx + 6.25 g. x2 4x 4 h. x2 + 20x + 10 i. x2 + x + 2 j. X 2-5X + P 2 2) k. x2 + 14x + 28 I. x2 18x 81
3. Determine the value of c needed to create a perfect square trinomial, then write the trinomial in factored form. a. x2 + 4x + b. x2 + 10x + c. x2 + 14x + d. x2 12x + e. x2 8x + f. x2 2x + g. x2 5x + h. x2 + 9x + I. x2 + 6.5x + 4. Complete the square to write the equation of a circle in standard form, and determine its center and radius. a. x2 + 14x + y2 8y = 1 b. 3x2 + 3y2 30x + 12y + 39 = 0 c. x2 + y2 + 4x 16y + 52 = 0 d. x2 + y2 + 2x + 18y + 1 = 0 e. x2 + y2 10x + 10y = 48 f. 7x2 + 7y2 70x 84y + 252 = 0