Name. Chapter 12: Circles


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1 Name Chapter 12: Circles
2 Chapter 12 Calendar Sun Mon Tue Wed Thu Fri Sat May (Friday) 14 Chapter 10/11 Assessment W Due HW Due Review 12.3 HW Due Review 19 / Review Quiz & 12.4 Practice HW Due Memorial DayNo School _.4 29 Completing the Square 12.5 HW Due 30 Chapter 12 Practice Test Completing the Square HW Due 31 Chapter 12 Review Final Review June 1 Chapter 12 Test 8 Final Review Final Review 12 Final Review FERP Due 13 1st & 2nd Hour Flnals 14 3rd & 4th Hour Finab 15 5th Hour Finals 16
3 12.1 Tangent Lines Warmup: I can... Identify tangent lines Use the right triangles that result from tangent lines to find missing lengths Homework: 12.1 Page 665 #14, 79, 1114, 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
4 Theorem 12.1If 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
5 A belt fits tightly around two circular pulleys, as shown. Find the distance between the centers of the pulleys. Theorem 12.2If 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
6 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
7 Theorem 12.3Two 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
8 I can... Identify tangent lines Use the right triangles that result from tangent lines to find missing lengths Homework: 12.1 Page 665 #14, 79, 1114, 17, Chords and Arcs Warmup: 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, 38, 1019, 26, 4246, 49,
9 A chord is a segment whose endpoints are on a circle. Theorem 12.4Within 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
10 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
11 Theorem 12.5Within a circle or in congruent circles: 1. Chords equidistant from the center are congruent 2. Congruent chords are equidistant from the center 17 9
12 Theorem 12.6In a circle, a diameter that is perpendicular to a chord bisects the chord and its arcs Theorem 12.7In a circle, a diameter that bisects a chord (that is not a diameter) is perpendicular to the chord Theorem 12.8In 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
13 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
14 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, 38, 1019, 26, 4246, 49,
15 12.3 Inscribed Angles Warmup: 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 # Inscribed anglean 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
16 Inscribed Angle TheoremThe measure of an inscribed angle is half the measure of its intercepted arc. 1 m/ B = nia
17 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
18 Theorem 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
19 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 # Angle Measures and Segment Lengths Warmup: 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 #115, 2024,
20 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 Secanta line that intersects a circle at two points Theorem 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)
21 Theorem 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 t
22 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
23 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 #115, 2024, Circles in the Coordinate Plane Warmup: I can... "Write an equation for a circle Find the center and radius of a circle Homework: 12.5 Page 697 #321 (every 3), odd, 45,
24 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
25 So how can we describe a circle in general? Write the standard equation of a circle with center (8, 0) and radius j
26 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)
27 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 #321 (every 3), odd, 45,
28 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 g. x2 4x 4 h. x2 + 20x + 10 i. x2 + x + 2 j. X 25X + P 2 2) k. x2 + 14x + 28 I. x2 18x 81
29 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. x x + 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 = 0
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