Uncut: Geometry Theory 15

Circles Finale (almost)

Volume 4

Practice Questions:

1. Two circles touch each other externally at Y. PYQ and RYS are two straight lines intersecting the first circle at P and R and the second circle at Q and S. If SY = 16 units, PY = 8 units, RY = 5 units, find QY.

2. Two circles touch each other internally at Y, YAB and YCD are two straight lines intersecting the larger circle at B and D and the smaller circle at A and C. If CD = 8 units, AB = 7units, YA = 5 units, find the lengths of YD and YC.

3. In the diagram given below, AB is a tangent to the circle and ACD is a secant. BP is the angle bisector of angle CBD meeting CD at P. If angle DAB is 20 degrees and angle CDB is 50 degrees, find the measure of angles angle CPB, angle ABC.

4. Three unequal circles are drawn such that each of those circles touch the other two externally. If the sides of triangle formed by joining the centres of three circles is given as 8 cm, 4 cm and 6 cm. Find the radii of the three circles.

5. In the diagram given below, PT is a tangent to the circle at D. If angle BDC = 30 degrees and angle CDT is 70 degrees, find the measure of angle BCD.

6. Two circles intersect and the length of common chord is 24 units. If their centers are 20 cm apart and radius of one of circle is 15 units, find the area (approximate) of the second circle.

7. Two circles of equal radii intersect each other. If their centers are 32 cm apart and the length of the common chord is 16 cm, find their radius.

8. Two circles having radii 16 and 30 units intersect orthogonally. If the distance between their centers is 34 units, find the length of the common chord.

29 thoughts on “Uncut: Geometry Theory 15”

  1. 1. 25.6
    2. 40/7 , 96/7
    3. 80 deg, 50 deg
    4. 1,3,5
    5. 80 deg
    6. 13/7 root615
    8. 8 root 5
    9. 480/17

  2. 1) 25.6
    2) YD=13.7 AND YC=5.7
    3) ANGLE ABC= 50 AND ANGLE CPB= 80
    4)1,3,5
    5) ANGLE BCD= 80
    6)13ROOT 615/14
    7)265 PIE
    8) 8 ROOT 5
    9) 480/ 17 OR 28.23

  3. 1:- QY= 25.6 units
    2:-YC= 5.7 units, YD= 13.7 units
    3:-anglE CPB=80 DEGREE,angle ABC=50 DEGREE
    4:-radii of the 3 circles are 1,5,3 units
    5:-angleBCD= 80 degree
    7:-area= 833 sq.units

  4. 1) 25.6 units
    2) 40/7 , 96/7
    3) 80degree, 50degree
    4) 1 cm , 3 cm , 5 cm
    5)80 degree
    6) 13root615 / 14
    7) 265 pie sq. unit
    8) 8 root 5
    9) 480/17 units

  5. 1. 25.6
    2. 40/7 , 96/7
    3. 80 deg, 50 deg
    4. 1,3,5
    5. 80 deg
    6. 13/7 root615
    8. 8 root 5
    9. 480/17

  6. 1.25.6
    2.YC=5.7
    YD=13.7
    3.angle CPB=80degrees
    angle ABC=50degrees
    4.1,3,5
    5.angle BCD=80degrees
    6.57root85/14
    7.could not solve.pls help sir
    8.8root 5
    9.240/7

  7. 1. 25.6
    2. YC= 40/7, YD= 96/7
    3. CPB=80 & ABC=50
    4. 1,3,5
    5. 80
    6. 13/14 ROOT615
    7. 265 PI SQ UNITS
    8. 8 ROOT5
    9. 240/17

  8. 1. QY= 25.6 units.
    2.YC= 5.7 units, YD= 13.7 units.
    3.anglE CPB=80 DEGREE,angle ABC=50 DEGREE.
    4.radii of the 3 circles are 1,5,3 units.
    5.angleBCD= 80 degree.
    6.AB=13/14root615 units.
    7.area= 833 sq.units.
    8.radius= 8root3 units.
    9.length of common chord=28.23 units.

  9. 1.25.6 units
    2.40/7, 96/7
    3.80, 50
    4.1,5,3
    5.80 degree
    6.13/14root615
    7.833 sq.unit
    8.8 root3
    9.28.23 units

  10. 1.QY=8.53
    2.YC=40/7 & YD=96/7
    3.Angle CPB=80
    4.Radii are 1,3,5
    5.Angle BCD=80
    7.Area = 265 pi square units
    8.Radius= 8root5
    9.Length of the chord 28.235

  11. 1.QY=8.53
    2.YC=40/7 & YD=96/7
    3.Angle CPB=80
    4.Radii are 1,3,5
    5.Angle BCD=80
    7.Area = 265square units
    8.Radius= 8root5
    9.Length of the chord 28.235

  12. ) QY= 25.6 units
    2)YC= 5.7 units, YD= 13.7 units
    3)anglE CPB=80,angle ABC=50
    4)radii of the 3 circles are 1,5,3 units
    5)angleBCD= 80 degree
    6)AB=13/14root615 units
    7)area= 833 sq.units
    8)??????????
    9)length of common chord=28.23 units

  13. 1.QY=8.53
    2.YC=40/7
    YD=96/7
    3.Angle CPB=80
    4.Radii are 1,3,5
    5.Angle BCD=80
    7.Area = 265 pi square units
    8.Radius= 8root5
    9.Length of the chord = 28.23

  14. 1.7.8
    PB=12.8
    2. 4:1
    3.13
    BC=14
    AC=15
    4. 3
    5. 10
    6. 2:1
    7. 5
    BE=3
    CF=7 units
    8.angleB=80 degree, angleC=55 degree
    9.angleAPB=angleABQ= 55 degree
    10.a)40 degree
    b)50 degree
    c)30 degree

  15. 1:: 25.6 units
    2:: 40/7, 96/7
    3:: 80, 50
    4:: 1,5,3
    5:: 80 degree
    6:: 13/14root615
    7:: 833 sq.unit
    8:: 8 root3
    9:: 28.23 units

  16. Ans1)25.6 uuits.
    Ans2)YC=5.7 units and YD=13.7 units.
    Ans3)CPB= 80 degree.
    Ans4)Radius of the circle = 1,3 and5 units.

  17. 1 25.6
    2 cy= 5.7
    dy= 13.7
    3 cpb= 70
    abc= 50
    4 1,3, 5
    5 bcd= 80
    6 13root615/14
    7 pi265
    8 8root5
    9 480/17

  18. 1) QY= 25.6 units
    2)YC= 5.7 units, YD= 13.7 units
    3)anglE CPB=80,angle ABC=50
    4)radii of the 3 circles are 1,5,3 units
    5)angleBCD= 80 degree
    6)AB=13/14root615 units

  19. 1. QY= 25.6 units
    2.YC= 5.7 units, YD= 13.7 units
    3.CPB=80 DEGREE, ABC=50 DEGREE
    4.1,5,3 units
    5.80 degree
    6.13/14root615 units
    7.833 sq.units
    8.8root3 units
    9.28.23 units

  20. Answers:
    A-1)25.6
    A-2)YC=5.7,YD=13.7
    A-3)angleCPB=80degree,angleABC=50degree
    A-4)1,5,3
    A-5)80degree
    A-6)13root615/2
    A-7)265pie
    A-8)8root5
    A-9)480/17

  21. 1. QY= 25.6 units.
    2.YC= 5.7 units, YD= 13.7 units.
    3.Angle CPB=80,angle ABC=50 .
    4.radii=1,5,3 units.
    5.angleBCD= 80.
    6.AB=13/14root615 units.
    7.?
    8.radius= 8root3 units.
    9.common chord=28.23 un
    Sir Please help with Q7.

  22. 1. QY= 25.6 units
    2.YC= 5.7 units, YD= 13.7 units
    3.anglE CPB=80 DEGREE,angle ABC=50 DEGREE
    4.radii of the 3 circles are 1,5,3 units
    5.angleBCD= 80 degree
    6.AB= 13 root153.75/7
    7.area= approx. 836 sq.units
    8.radius= 8root3 units
    9.length of common chord=28.23 units

  23. 1. 25.6
    2. YC= 40/7 YD= 96/7
    3. CPB=80 ABC=50
    4. 1, 3, 5
    5. 80
    6. 13/14 ROOT 615
    8. 8 ROOT 5
    9. 240/17

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