Circumradius of Triangle Solution

STEP 0: Pre-Calculation Summary
Formula Used
Circumradius of Triangle = (Side A of Triangle*Side B of Triangle*Side C of Triangle)/sqrt((Side A of Triangle+Side B of Triangle+Side C of Triangle)*(Side B of Triangle-Side A of Triangle+Side C of Triangle)*(Side A of Triangle-Side B of Triangle+Side C of Triangle)*(Side A of Triangle+Side B of Triangle-Side C of Triangle))
rc = (Sa*Sb*Sc)/sqrt((Sa+Sb+Sc)*(Sb-Sa+Sc)*(Sa-Sb+Sc)*(Sa+Sb-Sc))
This formula uses 1 Functions, 4 Variables
Functions Used
sqrt - A square root function is a function that takes a non-negative number as an input and returns the square root of the given input number., sqrt(Number)
Variables Used
Circumradius of Triangle - (Measured in Meter) - Circumradius of Triangle is the radius of a circumcircle touching each of the vertices of the Triangle.
Side A of Triangle - (Measured in Meter) - The Side A of Triangle is the length of the side A, of the three sides of the triangle. In other words, the side A of the Triangle is the side opposite to the angle A.
Side B of Triangle - (Measured in Meter) - The Side B of Triangle is the length of the side B of the three sides. In other words, the side Bof the Triangle is the side opposite to the angle B.
Side C of Triangle - (Measured in Meter) - The Side C of Triangle is the length of the side C of the three sides. In other words, side C of the Triangle is the side opposite to angle C.
STEP 1: Convert Input(s) to Base Unit
Side A of Triangle: 10 Meter --> 10 Meter No Conversion Required
Side B of Triangle: 14 Meter --> 14 Meter No Conversion Required
Side C of Triangle: 20 Meter --> 20 Meter No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
rc = (Sa*Sb*Sc)/sqrt((Sa+Sb+Sc)*(Sb-Sa+Sc)*(Sa-Sb+Sc)*(Sa+Sb-Sc)) --> (10*14*20)/sqrt((10+14+20)*(14-10+20)*(10-14+20)*(10+14-20))
Evaluating ... ...
rc = 10.7705054606916
STEP 3: Convert Result to Output's Unit
10.7705054606916 Meter --> No Conversion Required
FINAL ANSWER
10.7705054606916 10.77051 Meter <-- Circumradius of Triangle
(Calculation completed in 00.004 seconds)

Credits

Creator Image
Birla Institute of Technology & Science (BITS), Hyderabad
Venkata Sai Prasanna Aradhyula has created this Calculator and 10+ more calculators!
Verifier Image
Verified by Shweta Patil
Walchand College of Engineering (WCE), Sangli
Shweta Patil has verified this Calculator and 1100+ more calculators!

Radius of Triangle Calculators

Circumradius of Triangle
​ LaTeX ​ Go Circumradius of Triangle = (Side A of Triangle*Side B of Triangle*Side C of Triangle)/sqrt((Side A of Triangle+Side B of Triangle+Side C of Triangle)*(Side B of Triangle-Side A of Triangle+Side C of Triangle)*(Side A of Triangle-Side B of Triangle+Side C of Triangle)*(Side A of Triangle+Side B of Triangle-Side C of Triangle))
Circumradius of Triangle given Three Exradii and Inradius
​ LaTeX ​ Go Circumradius of Triangle = (Exradius Opposite to ∠A of Triangle+Exradius Opposite to ∠B of Triangle+Exradius Opposite to ∠C of Triangle-Inradius of Triangle)/4
Inradius of Triangle given Three Exradii
​ LaTeX ​ Go Inradius of Triangle = 1/(1/Exradius Opposite to ∠A of Triangle+1/Exradius Opposite to ∠B of Triangle+1/Exradius Opposite to ∠C of Triangle)
Circumradius of Triangle given One Side and its Opposite Angle
​ LaTeX ​ Go Circumradius of Triangle = Side A of Triangle/(2*sin(Angle A of Triangle))

Radius of Triangle Calculators

Circumradius of Triangle
​ LaTeX ​ Go Circumradius of Triangle = (Side A of Triangle*Side B of Triangle*Side C of Triangle)/sqrt((Side A of Triangle+Side B of Triangle+Side C of Triangle)*(Side B of Triangle-Side A of Triangle+Side C of Triangle)*(Side A of Triangle-Side B of Triangle+Side C of Triangle)*(Side A of Triangle+Side B of Triangle-Side C of Triangle))
Inradius of Triangle
​ LaTeX ​ Go Inradius of Triangle = sqrt((Side A of Triangle+Side B of Triangle+Side C of Triangle)*(Side B of Triangle+Side C of Triangle-Side A of Triangle)*(Side A of Triangle-Side B of Triangle+Side C of Triangle)*(Side A of Triangle+Side B of Triangle-Side C of Triangle))/(2*(Side A of Triangle+Side B of Triangle+Side C of Triangle))
Exradius Opposite to Angle A of Triangle
​ LaTeX ​ Go Exradius Opposite to ∠A of Triangle = sqrt((((Side A of Triangle+Side B of Triangle+Side C of Triangle)/2)*((Side A of Triangle-Side B of Triangle+Side C of Triangle)/2)*((Side A of Triangle+Side B of Triangle-Side C of Triangle)/2))/((Side B of Triangle+Side C of Triangle-Side A of Triangle)/2))

Circumradius of Triangle Formula

​LaTeX ​Go
Circumradius of Triangle = (Side A of Triangle*Side B of Triangle*Side C of Triangle)/sqrt((Side A of Triangle+Side B of Triangle+Side C of Triangle)*(Side B of Triangle-Side A of Triangle+Side C of Triangle)*(Side A of Triangle-Side B of Triangle+Side C of Triangle)*(Side A of Triangle+Side B of Triangle-Side C of Triangle))
rc = (Sa*Sb*Sc)/sqrt((Sa+Sb+Sc)*(Sb-Sa+Sc)*(Sa-Sb+Sc)*(Sa+Sb-Sc))

What is a Triangle?

A Triangle is a type of polygon, which have three sides and three vertices. This is a two-dimensional figure with three straight sides. A triangle is considered a 3-sided polygon. The sum of all the three angles of a triangle is equal to 180°. The triangle is contained in a single plane. Based on its sides and angle measurement, the triangle has six types.

What is a Circumcircle ?

Circumcircle is the circle that passes through all vertices (corner points) of a triangle. The center of the circumcircle is called the circumcenter, and the circle's radius is called the circumradius. The circumcenter of a triangle is defined as the point where the perpendicular bisectors of the sides of that particular triangle intersect.

How to Calculate Circumradius of Triangle?

Circumradius of Triangle calculator uses Circumradius of Triangle = (Side A of Triangle*Side B of Triangle*Side C of Triangle)/sqrt((Side A of Triangle+Side B of Triangle+Side C of Triangle)*(Side B of Triangle-Side A of Triangle+Side C of Triangle)*(Side A of Triangle-Side B of Triangle+Side C of Triangle)*(Side A of Triangle+Side B of Triangle-Side C of Triangle)) to calculate the Circumradius of Triangle, The Circumradius of Triangle formula is defined as the length of the radius of the circumcircle of the triangle, calculated using three sides of the Triangle. Circumradius of Triangle is denoted by rc symbol.

How to calculate Circumradius of Triangle using this online calculator? To use this online calculator for Circumradius of Triangle, enter Side A of Triangle (Sa), Side B of Triangle (Sb) & Side C of Triangle (Sc) and hit the calculate button. Here is how the Circumradius of Triangle calculation can be explained with given input values -> 10.77051 = (10*14*20)/sqrt((10+14+20)*(14-10+20)*(10-14+20)*(10+14-20)).

FAQ

What is Circumradius of Triangle?
The Circumradius of Triangle formula is defined as the length of the radius of the circumcircle of the triangle, calculated using three sides of the Triangle and is represented as rc = (Sa*Sb*Sc)/sqrt((Sa+Sb+Sc)*(Sb-Sa+Sc)*(Sa-Sb+Sc)*(Sa+Sb-Sc)) or Circumradius of Triangle = (Side A of Triangle*Side B of Triangle*Side C of Triangle)/sqrt((Side A of Triangle+Side B of Triangle+Side C of Triangle)*(Side B of Triangle-Side A of Triangle+Side C of Triangle)*(Side A of Triangle-Side B of Triangle+Side C of Triangle)*(Side A of Triangle+Side B of Triangle-Side C of Triangle)). The Side A of Triangle is the length of the side A, of the three sides of the triangle. In other words, the side A of the Triangle is the side opposite to the angle A, The Side B of Triangle is the length of the side B of the three sides. In other words, the side Bof the Triangle is the side opposite to the angle B & The Side C of Triangle is the length of the side C of the three sides. In other words, side C of the Triangle is the side opposite to angle C.
How to calculate Circumradius of Triangle?
The Circumradius of Triangle formula is defined as the length of the radius of the circumcircle of the triangle, calculated using three sides of the Triangle is calculated using Circumradius of Triangle = (Side A of Triangle*Side B of Triangle*Side C of Triangle)/sqrt((Side A of Triangle+Side B of Triangle+Side C of Triangle)*(Side B of Triangle-Side A of Triangle+Side C of Triangle)*(Side A of Triangle-Side B of Triangle+Side C of Triangle)*(Side A of Triangle+Side B of Triangle-Side C of Triangle)). To calculate Circumradius of Triangle, you need Side A of Triangle (Sa), Side B of Triangle (Sb) & Side C of Triangle (Sc). With our tool, you need to enter the respective value for Side A of Triangle, Side B of Triangle & Side C of Triangle and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.
How many ways are there to calculate Circumradius of Triangle?
In this formula, Circumradius of Triangle uses Side A of Triangle, Side B of Triangle & Side C of Triangle. We can use 2 other way(s) to calculate the same, which is/are as follows -
  • Circumradius of Triangle = Side A of Triangle/(2*sin(Angle A of Triangle))
  • Circumradius of Triangle = (Exradius Opposite to ∠A of Triangle+Exradius Opposite to ∠B of Triangle+Exradius Opposite to ∠C of Triangle-Inradius of Triangle)/4
Let Others Know
Facebook
Twitter
Reddit
LinkedIn
Email
WhatsApp
Copied!