Triangle in circle

Vertices of the triangle ABC lies on a circle with radius 3 so that it is divided into three parts in the ratio 4:4:4.

Calculate the circumference of the triangle ABC.

Correct answer:

o =  15.6

Step-by-step explanation:

$$\begin{gathered} {\mathrm{\Phi }}_1=360\cdot {\displaystyle \frac{4}{4+4+4}}=120^{\circ } \\ {\mathrm{\Phi }}_2=360\cdot {\displaystyle \frac{4}{4+4+4}}=120^{\circ } \\ {\mathrm{\Phi }}_3=360\cdot {\displaystyle \frac{4}{4+4+4}}=120^{\circ } \\ a=2\cdot 3\cdot \sin {\displaystyle \frac{{\mathrm{\Phi }}_1}{2}}=5.2 \\ b=2\cdot 3\cdot \sin {\displaystyle \frac{{\mathrm{\Phi }}_2}{2}}=5.2 \\ c=2\cdot 3\cdot \sin {\displaystyle \frac{{\mathrm{\Phi }}_3}{2}}=5.2 \\ o=a+b+c=15.6 \end{gathered}$$

Try another example

Related math problems and questions:

• Circumferential angle
  Vertices of the triangle ΔABC lay on the circle and divided into arcs in the ratio 7:8:7. Determine the size of the angles of the triangle ΔABC.
• MO - triangles
  On the AB and AC sides of the triangle ABC lies successive points E and F, on segment EF lie point D. The EF and BC lines are parallel and is true this ratio FD:DE = AE:EB = 2:1. The area of ABC triangle is 27 hectares and line segments EF, AD, and DB seg
• Nine-gon
  Calculate the perimeter of a regular nonagon (9-gon) inscribed in a circle with a radius 13 cm.
• Ratio of sides
  Calculate the area of a circle with the same circumference as the circumference of the rectangle inscribed with a circle with a radius of r 9 cm so that its sides are in ratio 2 to 7.
• Circle section
  Equilateral triangle with side 33 is inscribed circle section whose center is in one of the vertices of the triangle and the arc touches the opposite side. Calculate: a) the length of the arc b) the ratio betewwn the circumference to the circle sector and
• Pentagon
  Calculate the length of side, circumference and area of a regular pentagon, which is inscribed in a circle with radius r = 6 cm.
• Decagon
  Calculate the area and circumference of the regular decagon when its radius of a circle circumscribing is R = 1m
• Equilateral triangle ABC
  In the equilateral triangle ABC, K is the center of the AB side, the L point lies on one-third of the BC side near the point C, and the point M lies in the one-third of the side of the AC side closer to the point A. Find what part of the ABC triangle cont
• Hexagon A
  Calculate area of regular hexagon inscribed in circle with radius r=9 cm.
• Earth's circumference
  Calculate the Earth's circumference of the parallel 48 degrees and 10 minutes.
• Sines
  In ▵ ABC, if sin(α)=0.5 and sin(β)=0.6 calculate sin(γ)
• Triangle SAA
  The triangle has one side long 71 m and its two internal angles is 60°. Calculate the perimeter and area of the triangle.
• Pentadecagon
  Calculate the content of a regular 15-sides polygon inscribed in a circle with radius r = 4. Express the result to two decimal places.
• Circle described
  The radius of the circle described to the right triangle with 6 cm long leg is 5 cm. Calculate the circumference of this triangle.
• Equilateral triangle
  How long should be the minimum radius of the circular plate to be cut equilateral triangle with side 19 cm from it?
• Segment in a triangle
  In a triangle ABC with the side/AB/ = 24 cm is constructed middle segment/DE/ = 18 cm parallel to the side AB at a distance 1 cm from AB. Calculate the height of the triangle ABC to side AB.
• n-gon
  What is the side length of the regular 5-gon inscribed in a circle of radius 12 cm?