( ) Chapter 10 Review Question Answers. Find the value of x mhg. m B = 1 2 ( 80 - x) H x G. E 30 = 80 - x. x = 50. Find m AXB and m Y A D X 56

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1 hapter 10 Review Question nswers 1. ( ) Find the value of mhg 30 m = 1 2 ( 30) = 15 F 80 m = 1 2 ( 80 - ) H G E 30 = 80 - = Find m X and m Y m X = ( ) = X 56 Y m Y = ( ) = 32 aroody age 1 of 12

2 hapter 10 Review Question nswers 3. Find mq 70 = 1 ( 2 y + ) 140 = y + y X Y 30 = 1 ( 2 y - ) 60 = y - Q 200 = 2y y = 100 = Find the radius of a circle in which a 48 cm. chord is 8 cm closer to the center than a 40 cm chord. 40 ( 20) 2 + ( + 8) 2 = r 2 20 r r = r = r 2 ( 24) = r = r = r = r 2 16 = 112 = 7 r = 25cm ( 7, 24, 25 ) aroody age 2 of 12

3 hapter 10 Review Question nswers 5 Two circles intersect and have a common chord that measures 120 cm. The radii of the circles are 68 cm and 75 cm. Find the distance between their centers d = = 77 cm d 6 Find m S X m SXY = 1 2 ( 112) = ( 87 + m) = 56 2 Y m = = 25 aroody age 3 of 12

4 hapter 10 Review Question nswers 7. Find the radius of a circle if a 72-cm chord is 15 cm from the center Find ( - 2) = 8 2 = = 5 11 aroody age 4 of 12

5 hapter 10 Review Question nswers 9. If EFGH is regular, find the measure of E H m = = 45 G me = m E = 3( 45) = 135 F E 10. Given with radius 8, with radius 3, and = 13, find the length of the common eternal tangent aroody age 5 of 12

6 hapter 10 Review Question nswers 11. Two circles with radii 8 cm and 12 cm are 5 cm apart. Find the length of the common internal tangent The internal tangent is 15 ( the same as the third side of the red, which is a right ) 12.,, and are all tangent to each other. = 8, = 13, and = 11. Find the radii of the three s. ( 8 - ) + ( 11 - ) = = 13 6 = = Radius of = 3 Radius of = ( 8-3) = 5 Radius of = ( 11-3) = 8 aroody age 6 of 12

7 hapter 10 Review Question nswers 13. flatbed truck is hauling a cylindrical container with a diameter of 6 ft. Find, to the nearest hundredth, the length of a cable needed to hold down the container. 6 ft E Length of E = ( 2! ( 3) ) = 2! F Total length of cable = ( 2! + 6 3) "16.68 ft. 14. circular garbage can is wedged into a rectangular corner. The can has a diameter of 50 cm. a. Find the distance from the corner point to the point of contact of the can with the wall ( ) = 25 ( a side of a square) b. Find the distance from the corner point to the can ( ) Since we have a square, the diagonal is The radius is 25, so = cm aroody age 7 of 12

8 hapter 10 Review Question nswers 15. circular garbage can is wedged into a corner angled at 60. The can has a diameter of 46 cm. a. Find the distance from the corner point to the point of contact of the can with the wall ( ) = 23 3 ( longer side of ) b. Find the distance from the corner point to the point on the can that is closest to it ( ) Since we have a kite which is split into two s, the diagonal is 46. The radius is 23, so = = 23 cm Find the measure of a tangent-tangent angle if the measure of the major intercepted arc is 10 less than 4 times the measure of the minor intercepted arc. + ( 4-10) = = 370 = ( 4( 74) - 10) = 286 m = ( ) = 106 aroody age 8 of 12

9 hapter 10 Review Question nswers 17. quadrilateral is inscribed in a circle. Its vertices divide the circle into four arcs in the ratio 1:2:5:4. Find the measures of the angles of the quadrilateral = = = 30 m = ( ) = 75 m = ( ) = m = ( ) = 105 m = ( ) = T is a tangent segment. Find the radius of. 19. T Q = 5( 5 + 2) 225 = = 200 = 20 Find the radius of a circle if a central angle of 85 intercepts an arc with length of 17 feet. 17 = ( 2!r) = 2!r 36! = r aroody age 9 of 12

10 hapter 10 Review Question nswers 20. Given the information shown below, find the radius of the arc. 9 2 = = 3 = 27 iameter = 30 Radius = J is a tangent to. Find the measure of all the letters angles and arcs. a = 50 b = 20 c = 15 d = 130 e = 130 f = 25 g = 25 h = 45 i = 70 j = 35 k = 90 m = 35 b g e d 50 f 10 a k h m J j c i 90 aroody age 10 of 12

11 hapter 10 Review Question nswers 22. Given: T tangent at T T is midpoint of rove: T T T Statements Reasons 1. T tangent at T T is midpoint of 2. T is right 3. T is right 4. T T 1. Given 5. T T 5. efinition of midpoint of an arc 6. T T 6. s inscribed in arcs are 7. T T 7. ( 4, 5) radius to a point of tangency is to the tangent n inscribed in a semicircle is right ll right s are 23. (This is a hard one, but not all that long ~ 7 steps) Given: rove: & Q are internally tangent at T. :T = :T Q T S Statements Reasons 1. & Q are internally tangent at T. 2. raw tangent line TS 3. mt = mt 4. raw & 5. T T :T = :T 1. Given uiliary Lines rcs inscribed in the same ( tangent-chord) have the same measure 4. uiliary Lines 5. s inscribed in arcs of the same measure are congruent Side-Splitter Theorem aroody age 11 of 12

12 hapter 10 Review Question nswers 24. Given: & E are chords rove: ( ) ( ) = ( ) ( E) E Statements Reasons 1. & E are chords 2. raw E & 2. uiliary Lines 3. E 3. s inscribed in the same arc are s inscribed in the same arc are 5. E 5. ( 3, 4) 6. E = 7. ( ) ( ) = ( ) ( E) 1. Given 6. SST 7. Means-Etremes roducts Theorem aroody age 12 of 12

( ) Find the value of x mhg. H x G. Find m AXB and m Y A D X 56. Baroody Page 1 of 18

( ) Find the value of x mhg. H x G. Find m AXB and m Y A D X 56. Baroody Page 1 of 18 1. ( ) Find the value of x mhg 30 F 80 H x G E 2. Find m X and m Y 120 X 56 Y aroody age 1 of 18 3. Find mq X 70 30 Y Q 4. Find the radius of a circle in which a 48 cm. chord is 8 cm closer to the center

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