Circumradius of Triangle given Three Exradii and Inradius Calculator

✖The Exradius Opposite to ∠A of triangle is the radius of circle formed with center as point of intersection of internal angle bisector of ∠A and external angle bisectors of other two angles.ⓘ Exradius Opposite to ∠A of Triangle [r_e(∠A)]			+10% -10%
✖Exradius Opposite to ∠B of triangle is the radius of circle formed with center as point of intersection of internal angle bisector of ∠B and external angle bisectors of other two angles.ⓘ Exradius Opposite to ∠B of Triangle [r_e(∠B)]			+10% -10%
✖Exradius Opposite to ∠C of triangle is the radius of circle formed with center as point of intersection of internal angle bisector of ∠C and external angle bisectors of other two angles.ⓘ Exradius Opposite to ∠C of Triangle [r_e(∠C)]			+10% -10%
✖Inradius of Triangle is defined as the radius of the circle which is inscribed inside the Triangle.ⓘ Inradius of Triangle [r_i]			+10% -10%

✖Circumradius of Triangle is the radius of a circumcircle touching each of the vertices of the Triangle.ⓘ Circumradius of Triangle given Three Exradii and Inradius [r_c]

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Circumradius of Triangle given Three Exradii and Inradius Solution

STEP 0: Pre-Calculation Summary

Formula Used

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
r_c = (r_e(∠A)+r_e(∠B)+r_e(∠C)-r_i)/4
This formula uses 5 Variables

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.
Exradius Opposite to ∠A of Triangle - (Measured in Meter) - The Exradius Opposite to ∠A of triangle is the radius of circle formed with center as point of intersection of internal angle bisector of ∠A and external angle bisectors of other two angles.
Exradius Opposite to ∠B of Triangle - (Measured in Meter) - Exradius Opposite to ∠B of triangle is the radius of circle formed with center as point of intersection of internal angle bisector of ∠B and external angle bisectors of other two angles.
Exradius Opposite to ∠C of Triangle - (Measured in Meter) - Exradius Opposite to ∠C of triangle is the radius of circle formed with center as point of intersection of internal angle bisector of ∠C and external angle bisectors of other two angles.
Inradius of Triangle - (Measured in Meter) - Inradius of Triangle is defined as the radius of the circle which is inscribed inside the Triangle.

STEP 1: Convert Input(s) to Base Unit

Exradius Opposite to ∠A of Triangle: 5 Meter --> 5 Meter No Conversion Required
Exradius Opposite to ∠B of Triangle: 8 Meter --> 8 Meter No Conversion Required
Exradius Opposite to ∠C of Triangle: 32 Meter --> 32 Meter No Conversion Required
Inradius of Triangle: 3 Meter --> 3 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

r_c = (r_e(∠A)+r_e(∠B)+r_e(∠C)-r_i)/4 --> (5+8+32-3)/4

Evaluating ... ...

r_c = 10.5

STEP 3: Convert Result to Output's Unit

10.5 Meter --> No Conversion Required

FINAL ANSWER

10.5 Meter <-- Circumradius of Triangle

(Calculation completed in 00.020 seconds)

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Birla Institute of Technology & Science (BITS), Hyderabad

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< 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))

Circumradius of Triangle given Three Exradii and Inradius Formula

LaTeX Go

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 Circumradius?

Circumradius is the radius of the circumcircle, which always passes through all three vertices of a triangle. Its center is at the point where all the perpendicular bisectors of the triangle's sides meet. This center is called the circumcenter.

How to Calculate Circumradius of Triangle given Three Exradii and Inradius?

Circumradius of Triangle given Three Exradii and Inradius calculator uses 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 to calculate the Circumradius of Triangle, The Circumradius of Triangle given Three Exradii and Inradius formula is defined as the length of the radius of the circumcircle of the triangle, calculated using three exradii and the inradius of the Triangle. Circumradius of Triangle is denoted by r_c symbol.

How to calculate Circumradius of Triangle given Three Exradii and Inradius using this online calculator? To use this online calculator for Circumradius of Triangle given Three Exradii and Inradius, enter Exradius Opposite to ∠A of Triangle (r_e(∠A)), Exradius Opposite to ∠B of Triangle (r_e(∠B)), Exradius Opposite to ∠C of Triangle (r_e(∠C)) & Inradius of Triangle (r_i) and hit the calculate button. Here is how the Circumradius of Triangle given Three Exradii and Inradius calculation can be explained with given input values -> 10.5 = (5+8+32-3)/4.

FAQ

What is Circumradius of Triangle given Three Exradii and Inradius?

The Circumradius of Triangle given Three Exradii and Inradius formula is defined as the length of the radius of the circumcircle of the triangle, calculated using three exradii and the inradius of the Triangle and is represented as r_c = (r_e(∠A)+r_e(∠B)+r_e(∠C)-r_i)/4 or 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. The Exradius Opposite to ∠A of triangle is the radius of circle formed with center as point of intersection of internal angle bisector of ∠A and external angle bisectors of other two angles, Exradius Opposite to ∠B of triangle is the radius of circle formed with center as point of intersection of internal angle bisector of ∠B and external angle bisectors of other two angles, Exradius Opposite to ∠C of triangle is the radius of circle formed with center as point of intersection of internal angle bisector of ∠C and external angle bisectors of other two angles & Inradius of Triangle is defined as the radius of the circle which is inscribed inside the Triangle.

How to calculate Circumradius of Triangle given Three Exradii and Inradius?

The Circumradius of Triangle given Three Exradii and Inradius formula is defined as the length of the radius of the circumcircle of the triangle, calculated using three exradii and the inradius of the Triangle is calculated using 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. To calculate Circumradius of Triangle given Three Exradii and Inradius, you need Exradius Opposite to ∠A of Triangle (r_e(∠A)), Exradius Opposite to ∠B of Triangle (r_e(∠B)), Exradius Opposite to ∠C of Triangle (r_e(∠C)) & Inradius of Triangle (r_i). With our tool, you need to enter the respective value for Exradius Opposite to ∠A of Triangle, Exradius Opposite to ∠B of Triangle, Exradius Opposite to ∠C of Triangle & Inradius 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 Exradius Opposite to ∠A of Triangle, Exradius Opposite to ∠B of Triangle, Exradius Opposite to ∠C of Triangle & Inradius 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 = (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))

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