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Big Idea: 1. The altitude bisects the base of an isosceles triangle (#1) 2. The distance that a segment is from a point is measured as a perpendicular distance (#1) 3. The perpendicular bisector of a chord passes through the center of the circle (#2) If a segment is perpendicular to a chord, then it bisects it (#2) If a segment bisects a chord, then it is perpendicular to it (#2) 4. If a chord is equidistant from the center of the circle as another chord, the chords are congruent. (#3) If a chord is smaller than another chord, it is further away from the center of the circle. If it is larger, it is closer to the center of the circle. (#4) 5. The largest chord of a circle is the diameter (#5) 6. The length of an arc is different than the measure of an arc (#6) 7. An arc measuring less than 180 degrees can be named by 2 letters, an arc named by 3 letters is greater than 180 degrees. (#6) 8. The measure of an intercepted arc is the same as the measure of its central angle (#6) 9. The measure of an inscribed angle is ½ the measure of its intercepted arc (#9) 10. If two central angles have the same measure, then so do their intercepted arcs. (#6) If two arcs have the same measure, then so do their central angles (#6) If 2 chords have the same measure, then so do their central angles and intercepted arcs (#7) ( x − h) 2 + ( y − k ) 2 = r 2 11. The equation of a circle is (#8) 12. Secants intersect a circle at 2 points. (#10) 13. A tangent intersects a circle at 1 point and is perpendicular to the radius intersecting it. (#10) 14. The slope of a tangent is the negative reciprocal of the slope of the radius/diameter tangent to it (#11) Geometry Unit 10 Big Idea Problems _____________________________________ BC 1. How far is from A Name A ? 50° B 50° 10 C BIG IDEA: Geometry Unit 10 Big Idea Problems _____________________________________ 2. dA Name with radius of 41. D AD ⊥ BC ED = 1 , BC C E Find A BIG IDEA: B Geometry Unit 10 Big Idea Problems _____________________________________ 3. dA Name BC with radius of 5. Which chord is bigger, or ED E ? 3 A B BIG IDEA: D 8 C Geometry Unit 10 Big Idea Problems _____________________________________ Name 50 B C A 78 E D 4. dA BC with radius of 65. Which chord is closer to the center of the circle, or ED ? BIG IDEA: Geometry Unit 10 Big Idea Problems _____________________________________ 5. Name Draw in the longest chord of this circle. Justify why you think it is longest and what characteristics it has that makes it the longest? BIG IDEA: Geometry Unit 10 Big Idea Problems _____________________________________ Name What is the area of the sector BAC? A B C 120° 4 feet BIG IDEA: Geometry Unit 10 Big Idea Problems _____________________________________ 6. If » = 110° KE , the radius of circle I is 6, and a. What is the length of Name RKIR ≅ 110o , E ¼ KER I ? K b. What is the measure of ¼ KER ? R c. How do BIG IDEA: ¼ ¼ KR ER , and ¼ KE compare in measure? Geometry Unit 10 Big Idea Problems _____________________________________ 7. If RKIR ≅ 110o Find 10 2 ,radius = and KR = 20 Name E EK I R K BIG IDEA: (x, y) 5 (7,8) Geometry Unit 10 Big Idea Problems Name _____________________________________ 8. a. Write an expression for the length of horizontal segment b. Write an expression for the length of the vertical segment c. Write an equation for the relationship of the horizontal and vertical segments as compared to the hypotenuse d. Write a general relationship for the equation of a circle not centered at (0,0) BIG IDEA: A C B D Geometry Unit 10 Big Idea Problems _____________________________________ ¼ BDC RCDB 9. Find the measure of , Name ¼ DC and 24 12.5 7 16.9° BIG IDEA: Geometry Unit 10 Group Challenge Opener _____________________________________ Name Circle Alpha has a radius of 10 centimeters. Circle Beta has a radius of 15 centimeters. A chord of length 8 centimeters is drawn on each circle. Is the chord on circle Alpha or the chord on circle Beta closer to the center of its circle? Distance of Chords Task Card Side #1 Task: Your group’s task is to solve the following 2 problems and justify your work to Mr. Jhunjhunwala in written form. Your group will earn today’s point by accurately solving the problem and providing a clear explanation of your solution. Individual Accountability: Each group member must have the work completed on their own task card. Group Accountability: One group member’s written justification will be assessed by Mr. Jhunjhunwala to earn the team point for the day. Mr. Jhunjhunwala may ask follow up questions of team members as well. When you are ready for Mr. Jhunjhunwala to assess your group’s work, call him over. Problem #1: ( x − 3) 2 + ( y − 5 ) = 169 2 The equation for circle A is ( x + 2) 2 + ( y − 1) = 25 2 The equation for circle B is A chord of length 24 cm is drawn on circle A. A chord of length 6 cm is drawn on circle B. Is the chord on circle A or the chord on circle B closer to the center of its circle? Solution and justification: Distance of Chords Task Card Side #2 Task: Your group’s task is to solve the following 2 problems and justify your work to Mr. Jhunjhunwala in written form. Your group will earn today’s point by accurately solving the problem and providing a clear explanation of your solution. Individual Accountability: Each group member must have the work completed on their own task card. Group Accountability: One group member’s written justification will be assessed by Mr. Jhunjhunwala to earn the team point for the day. Mr. Jhunjhunwala may ask follow up questions of team members as well. When you are ready for Mr. Jhunjhunwala to assess your group’s work, call him over. Problem #2: ( x − 125) 2 + ( y − 130 ) = 4225 2 The equation for circle A is A chord of length 120 cm is drawn on circle A. A second chord of length 78 cm is also drawn on circle A. Which chord is closer to the center of the circle? By how much is it closer? Solution and justification: Distance of Chords CHALLENGE CARD Task: Your group’s task is to solve the following problem and justify your work to Mr. Jhunjhunwala in written form. Your group will earn a bonus point for today by accurately solving the problem and providing a clear explanation of your solution. Individual Accountability: Each group member must have the work completed on their own task card. Group Accountability: One group member’s written justification will be assessed by Mr. Jhunjhunwala to earn the team point for the day. Mr. Jhunjhunwala may ask follow up questions of team members as well. When you are ready for Mr. Jhunjhunwala to assess your group’s work, call him over. Problem: Two chords are ten cm from the center of a circle. 7 x 2 − 15 The first chord has a length of long is the radius of the circle? Solution and justification: 16x . The second chord has a length of . How long is each cord? How Geometry Unit 10 Week 1 Group Quiz _____________________________________ Name I will select one of your group’s papers, and grade it. This will be the group’s grade on the quiz, so be sure to check everyone’s work. You will also take a very similar quiz so be sure you agree with and understand all the problems. 1. This is a circle w/ center at B. ABD = 30 Find the measure of each arc. (I am NOT asking you to find the length!!!) » AD » DC D = ______ 30° A = ______ ¼ AEC ¼ DCA B 8 = ______ E = ______ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ I 2. This is a circle w/ center at F. H GH = HI = IJ J GK = KJ » = 54° GH Find G F ¼ IJK K C (OVER) 3. A chord is 72 cm long. The chord is 15 cm from the center of the circle. How long is the radius of the circle? ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ y-axis x-axis C D B 4. BD is a diameter of B = (0, 12) eC D = (8, 12) Complete the equation for this circle: ( x − ____ ) 2 + ( y − ____ ) = _____ 2 Geometry Unit 10 Week 1 Quiz #1 Name _____________________________________ y-axis x-axis C D B 1. BD is a diameter of B = (0, 7) eC D = (20, 7) Write the equation for this circle: 2. This is a circle w/ center at B. ABD = 45 D Find the measure of each arc. (I am NOT asking you to find the length!!!) ¼ ADC = ______ 45° A B 8 E C » DC ¼ AD = ______ = ______ ¼ DCA = ______ (OVER) 3. A chord is 48 cm long. The chord is 7 cm from the center of the circle. How long is the radius of the circle? ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ I 4. This is a circle w/ center at F. H GH = HI = IJ J GK = KJ ¼ GH = 58° Find G F ¼ IJK K Geometry Unit 10 Big Idea Problems Definitions: Name A secant line intersects a curve(or circle) in exactly 2 points A tangent line intersects a curve(or circle) at exactly 1 point _____________________________________ 10. Lines suur AB suur AC and If the radius of circle a. are tangent to circle D is 7, and D . AD = 25 Find AB D C B b. Find AC A » CB CHALLENGE: Find the measure of BIG IDEA: Geometry Unit 10 Big Idea Problems _____________________________________ 10. Lines suur AB suur AC and are tangent to circle D Name . If the coordinates of D are (15, 50) and the coordinates of B are(22, 26) a. What is the slope of BD ? D C B b. What is the slope of AB ? A CHALLENGE: What are possible coordinates of A? BIG IDEA: Geometry Unit 10 Cumulative Problems _____________________________________ 1. Segment ZY AB is tangent to Circle Q at the midpoint of Name AB . Segment ZY is tangent to Circle D at the midpoint of . AB = 18 and ZY = 20. If AQ = 15 and ZD = 14, which circle is larger? Justify your answer. Geometry Unit 10 Cumulative Problems _____________________________________ Name 40° 2. Two chords form an inscribed angle that intercepts an arc of measure angle? . What is the measure of the inscribed Geometry Unit 10 Cumulative Problems _____________________________________ 3. A diagonal XY and chord XZ Name form an inscribed angle. PX of and the circle is point Z. The measure of arc YP, YX, and XP. – 3) 2 + is (y Find: The length of » PR Find: The measure of » PR + 18 ) 2 = 64 QP . ∠ 60° PSR = . If the radius of the circle is 5, find the length of Name 4. The equation of a circle Q is the circle, and the measure of is a tangent to the circle at point Y. The intersection YZ 120° Geometry Unit 10 Cumulative Problems _____________________________________ (x YP . QR and are both radii. S is another point on Find: The area of Sector QPR Geometry Unit 10 Cumulative Problems _____________________________________ 5. Name Circle L is four times as big as circle Q. The left side of Circle L is tangent to the right side of Circle Q. Write the equation of Circle L.