Geometry problem...?

Question

Hi-
I'm having trouble figuring out a certain problem...
I have an equilateral triangle with each side length of 10 and the triangle is inscribed in a circle. I need to find the distance from the center of the circle to the midpoint of any side.

Any suggestions?

Thanks.

Also, if someone could tell me how to work that out on paper that would be great. I need a precise explanation.

Thanks again.

Answer 1

Draw the line you want to determine. Then draw another line from the center of the circle to one of the adjoining angles in the triangle. You just bisected the angle in the triangle, making the smaller angle = 30°. You also know that the adjacent side is 5, so you use the tangent function that says:

x/5 = tan(30)

Can you take it from here?

Answer 2

Given triangle ABC inscribed in circle X, with AB=AC=BC=10. Draw a line through the circle that contains line segment AX, which is a radius of the circle. This line intersects the other side of the circle at a point D, and bisects segment BC at point E, which is its midpoint.

Now, AD is perpendicular to BC, so triangle XEC is a right triangle. Because triangle ABC is equilateral, angle ACB is 60 degrees, and because line XC bisects it, angle XCE is 30 degrees. Because triangle XEC is a 30-60-90 triangle, its sides are in the ratio 1:√3:2. Because E is the midpoint of BC, EC=5 and XE (the distance you're looking for) is 5/√3, or 5/3(√3).

Answer 3

In an equilateral triangle, the altitude, median and perpendicular bisectors of the sides are all the same.

Since the altitude is the longer lleg of a 30-60-90 degree triangle it is = 1/2side*sqrt(3) = 5sqrt(3).

Since the altitudes are also perpendicular bisectors they meet at the circumcenter.

Since the altitude is also a median they meet at a point that is 2/3 of the way from the vertex.

Thus the distance from the circumcenter to the midpoint of any side is 1/3 *5*sqrt(3) = (5/3)sqrt(3)

Answer 4

I believe to do this you will have to find the dimmensions of the triangle. Being all sides are equal. Take and draw a line down the center of the triangle. You know the hypotenuse and by divinding the number in 2 you know b. So you use this formula and solve for A. Whatever B squared is subtract from the hypotenuse squared to find A squared.

Answer 5

Find the distance from the center of the triangle one of its points. You can do this by using the Pythagorean theorem. You have a and c (one edge of the triangle and half of another edge) which are 5 and 10. Using a(squared) plus b(squared) equals c(squared) you get 5(squared) plus b(squared) equals 10(squared). So 25 plus b(squared) is 100. B(squared) then equals 75. So b equals the square root of 75 (can't do that one in my head. =D). This is the length from one edge of the triangle to a point of the triangle Cut this in half and you have your answer!

So put simply, your answer is the square root of 75 divided by two.

Hope this came in time to help!

Answer 6

I'd try the first link, the second has a lot of formulas, but the first describes everything.

the calculator give this as an answer. Inscribed Circle Radius (r) = 2.8867513459481

I'd still check it out and get the formulas they'll help you with any other problems you have.

Answer 7

I keep in mind that there is a thorem that if the two components of a traingle are equivalent then the perspective opposite to them are additionally comparable. Please see the thorem. So the bisectors make a isoscele traingle with the area in between the angles have been getting bisected.i will later write you the info of the theorm. by way of fact the each and each a million/2 of the angles are equivalent, then the finished angles are equivalent. here you got here across the two angles are equivalent. As in line with definition: in a traingle if the two angles are equivalent, then that traingle is named a isoscele traingle.

Answer 8

the altitude of the triangle or just proportions of the triangle that you know the lenght and that should be it