What is the relationship between diameter of circle and a side of equilateral triangle in which it's inscribd?

Question

If a circle is inscribed inside an equilateral triangle, how many times the diameter will be one of the triangle's sides?

Answer 1

length of one side of triangle ( L)= sqrt(3) * dia. of circle

Answer 2

You just asked about the relation so I am not giving the working.

The relation is L = sqrt(3) x D

Where L is the length of the triangle
D is the diameter of the circle.

It is pronounced as follows:
The length of the side of the triangle is equal to root three times the diameter.

Hope you can understand this.

Answer 3

for the reason that it is an equilateral triangle, each perspective is a similar as 60 degree. as a results of the indisputable fact that is likewise inscribed equilateral triangle, you could draw a bisector line (perpendicular bisectors) from each vertex to the option area. All 3 strains will intersect on the middle to create 6 equivalent divisions and each perspective is 60 degree on the middle of the circle. Now you also discover each vertex of the triangle is bisected by using 30 degree each. Now take only one piece of accurate triangle between 6. One area is 0.5 of the area of the equilateral triangle that is s/2. the hypotenuse is radius of the circle, skill 0.5 of the diameter = d/2 the right triangle is 30, 60, ninety particular accurate triangle. making use of trigonometry, cos 30 =adjoining area /hypotenuse meaning 0.866 = s/2 / d/2 once you simplify 0.866 = s/d (by using eliminating a similar denominators) So the relation between the diameter and the area is s = 0.866 d --------------------------------------... for the reason that it is 30, 60, ninety particular triangle, you should use the formula in ratio format a million x : sq. root 3 x: 2x we favor opposite of 60 degree area. s = sq. root of three (d/2) s = a million.732 (d/2) s = 0.866 d --------------------------------------...

Answer 4

I believe that the diameter of the sphere should be 2-thirds the length of the side of the equilateral triangle.

Answer 5

If you draw a line from the diameter to all three angles of the triangle you will get three iso triangles with the radii as the side. If this is a homework problem you should have some other information to help you once you get those information.

Answer 6

diameter = (1/sqrt3) times the side of the equilateral triangle

Answer 7

None. However, each of the sides of the triangle is a chord.

Answer 8

There is a relationship. I don't feel like copying it, so check out this source for what you need. If it's homework, then reading this should tell you more than you ever wanted to know.

Answer 9

Thank God i am done with school. Thank you for reminding me.