What is the formula ?

Triangles don't have radii, so I don't know what you mean by "the radius of a triangle". As for finding the radius of a circle, that will depend upon what information has been provided to you.

Please reply with the complete text of the exercise you are working on. Thank you.

Eliz.
 
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The_Rose said:
What is the formula for finding the radius of a circle.
If you're given a circle with no info and want to find the radius:
1: fold it forming 2 half circles
2: unfold it
3: take your ruler and measure the length of the "fold line" created
by steps 1 and 2 above

Ahem!

Post Scriptum: Do not forget to properly wrap up your task
by dividing the length in step 3 by 2.
 
What is the formula?

Might you be seeking the radius of a triangles inscribed or circumscbibed circles?

*--Incenter
The incenter is the point where the three angle bisectors intersect and is the center of the incircle.

*--Circumcenter
The circumcenter is the intersection of the perpendicular bisectors of the three sides of the triangle and the center of the circumscribed circle about the triangle.

*--Excenters
The points of intersection of an internal bisector of an interior angle at one vertex and the bisectors of the exterior angles of the other two vertices.

*--Incircle
The internal circle tangent to the three sides and the incenter as center.
The radius of the inscribed circle is r = A/s where A = the area of the triangle and s = the semi-perimeter = (a + b + c)/2, a, b, and c being the three sides.
The radius of the inscribed circle may also be derived from r = ab/(a + b + c).
The radius of the inscribed circle may also be derived from the particular m and n used in deriving a Pythagoraen Triple triangle by r = n(m - n).
If x, y, and z are the points of contact of the incircle with the sides of the triangle A, B, C, then Cx = Cy = s - c, Bx = Bz = s - b, and Ay = Az = s - a.

*--Circumcircle
The external circle touching the three vertices of a triangle with center at the circumcenter.
The radius of the circumcircle is R = abc/4A, a, b, and c being the three sides and A being the area of the triangle.
Second Law of Sines - With R = the circumcircle radius, a/sinA = b/sinB = c/sinC = 2R.

*--Excircles
The excircles, centered at the excenters, lie outside of the triangle and touch the three sides, one side of the triangle externally and two sides extended outside the triangle.

*--Incircle-Excircle Relationship
For an incircle radius of r and excircle radii of ra, rb, and rc, 1/r = 1/ra + 1/rb + 1/rc.

*--Excircle-Circumcircle Relationship
For a circumcircle radius of R, ra + rb + rc - r = 4R.

*--The incircle radius r, the circumcircle radius R, and the distance between the two centers s, are related to one another by R^2 = s^2 + 2Rr.
 
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