Wednesday

July 23, 2014

July 23, 2014

Posted by **buzz** on Saturday, May 18, 2013 at 6:50pm.

- geomerty -
**MathMate**, Saturday, May 18, 2013 at 7:04pmThere are different ways to solve for the circumscribed radius, depending on which part of geometry you are working on.

The most basic calculation taking advantage that the triangle ABC is equilateral is to construct a perpendicular bisector on side BC such that ABD is a right triangle right-angled at D.

AD is then the median, and the radius of the circumscribed circle is 2/3 of AD.

Using Pythagoras Theorem,

AD=sqrt(AB^2-BD^2)=sqrt(18^2-9^2)=sqrt(243)=9sqrt(3).

The radius of the circumscribed circle is therefore (2/3)*9sqrt(3)=6sqrt(3).

A more general method is

radius of circumscribed circle

=a/(2sin(A))

where a is any side of the triangle, and

A is the angle opposite side a.

Applied to the given equilateral triangle,

a=18

A=60°

so

r=18/(2sin(60)=6sqrt(3)

**Related Questions**

geometry - Find the area of a circle circumscribed about an equilateral triangle...

Geometry - Problem : Howm do you find the area of a circle circumscribed about a...

geometry - Open that link please please help me with my assignments 1. in the ...

Geometry - Bob - Problem : Howm do you find the area of a circle circumscribed ...

geomerty - two sides of a triangle have lengths 45 inches and 50 inches. How ...

mathematics - if a circle has a radius of 6 inches,what will the area of the ...

GEOMETRY URGENT PLEASE - (imageshack)(.)us(/)photo (/) my-images (/)42(/)2vja. ...

geometry PLEASE - imageshack(.)(us)/photo/my-images/42/2vja.jpg/ Open that link ...

Geometry - A circle has a radius of 6 inches. The circumscribed equilateral ...

GEOMETRY - Here are the figures. file:///C:/Users/ALIZAJOY/Pictures/Untitled....