Five circles

On the line segment CD = 6 there are 5 circles with radius one at regular intervals. Find the lengths of the lines AD, AF, AG, BD, and CE

Correct result:

d =  4.5826
f =  2.1794
g =  3.1225
b =  3.6056
c =  2.6458

Solution:

r=1 h=v(A,CD) AS1 S2=Δ111,α=β=γ=60, h=3/2 r=3/2 10.866  x1=(4+1/2) r=(4+1/2) 1=92=4.5 d=AD d=x12+h2=4.52+0.8662=21=4.5826
f=AE  x2=4/2 r=4/2 1=2  f=x22+h2=22+0.8662=2.1794
g=AG x3=6/2 r=6/2 1=3 g=x32+h2=32+0.8662=3.1225
b=BD x4=7/2 r=7/2 1=72=3.5 b=x42+h2=3.52+0.8662=13=3.6056
c=CE x5=5/2 r=5/2 1=52=2.5 c=x52+h2=2.52+0.8662=7=2.6458



We would be pleased if you find an error in the word problem, spelling mistakes, or inaccuracies and send it to us. Thank you!






Showing 0 comments:
avatar




Tips to related online calculators
Do you want to convert length units?
Pythagorean theorem is the base for the right triangle calculator.
See also our trigonometric triangle calculator.

 
We encourage you to watch this tutorial video on this math problem: video1   video2

Next similar math problems:

  • Triangular pyramid
    triangularPyramid A regular tetrahedron is a triangular pyramid whose base and walls are identical equilateral triangles. Calculate the height of this body if the edge length is a = 8 cm
  • Nonagon
    9gon Calculate the area and perimeter of a regular nonagon if its radius of inscribed circle is r = 10cm
  • Pentagon
    5gon Calculate the length of side, circumference and area of a regular pentagon, which is inscribed in a circle with radius r = 6 cm.
  • ABCD square
    s1 In the ABCD square, the X point lies on the diagonal AC. The length of the XC is three times the length of the AX segment. Point S is the center of the AB side. The length of the AB side is 1 cm. What is the length of the XS segment?
  • Concentric circles and chord
    tetiva2 In a circle with a diameter d = 10 cm, a chord with a length of 6 cm is constructed. What radius have the concentric circle while touch this chord?
  • Secret treasure
    max_cylinder_pyramid Scouts have a tent in the shape of a regular quadrilateral pyramid with a side of the base 4 m and a height of 3 m. Determine the radius r (and height h) of the container so that they can hide the largest possible treasure.
  • Top of the tower
    veza The top of the tower has the shape of a regular hexagonal pyramid. The base edge has a length of 1.2 m, the pyramid height is 1.6 m. How many square meters of sheet metal is needed to cover the top of the tower if 15% extra sheet metal is needed for joint
  • Rectangular trapezoid
    right-trapezium-figure The ABCD rectangular trapezoid with the AB and CD bases is divided by the diagonal AC into two equilateral rectangular triangles. The length of the diagonal AC is 62cm. Calculate trapezium area in cm square and calculate how many differs perimeters of the
  • Hexagon cut pyramid
    truncated_hexa_pyramid Calculate the volume of a regular 6-sided cut pyramid if the bottom edge is 30 cm, the top edge us 12 cm, and the side edge length is 41 cm.
  • Sailboat
    Plachetnice The 20 m long sailboat has an 8 m high mast in the middle of the deck. The top of the mast is fixed to the bow and stern with a steel cable. Determine how much cable is needed to secure the mast and what angle the cable will make with the ship's deck.
  • Chord
    chord In a circle with radius r=60 cm is chord 4× longer than its distance from the center. What is the length of the chord?
  • Circle chord
    circles_6 Calculate the length of the chord of the circle with radius r = 10 cm, length of which is equal to the distance from the center of the circle.
  • Circle and square
    square_axes An ABCD square with a side length of 100 mm is given. Calculate the radius of the circle that passes through the vertices B, C and the center of the side AD.
  • A rectangle 2
    rectangles A rectangle has a diagonal length of 74cm. Its side lengths are in ratio 5:3. Find its side lengths.
  • Dodecagon
    clocks Calculate the size of the smaller of the angles determined by lines A1 A4 and A2 A10 in the regular dodecagon A1A2A3. .. A12. Express the result in degrees.
  • Points on circle
    coordinates_circle In the Cartesian coordinate system with the origin O is a sketched circle k /O; r=2 cm/. Write all the points that lie on a circle k and whose coordinates are integers. Write all the points that lie on the circle I / O; r=5 cm / and whose coordinates are
  • A cylinder
    string A cylinder 108 cm high has a circumference of 24 cm. A string makes exactly 6 complete turns around the cylinder while its two ends touch the cylinder's top and bottom. (forming a spiral around the cylinder). How long is the string in cm?