Inradius of Triangle given Three Exradii 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 given Three Exradii [r_i]

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Formula

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Inradius of Triangle given Three Exradii

Formula

`"r"_{"i"} = 1/(1/"r"_{"e(∠A)"}+1/"r"_{"e(∠B)"}+1/"r"_{"e(∠C)"})`

Example

`"2.807018m"=1/(1/"5m"+1/"8m"+1/"32m")`

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Inradius of Triangle given Three Exradii Solution

STEP 0: Pre-Calculation Summary

Formula Used

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)
r_i = 1/(1/r_e(∠A)+1/r_e(∠B)+1/r_e(∠C))
This formula uses 4 Variables

Variables Used

Inradius of Triangle - (Measured in Meter) - Inradius of Triangle is defined as the radius of the circle which is inscribed inside 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.

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

STEP 2: Evaluate Formula

Substituting Input Values in Formula

r_i = 1/(1/r_e(∠A)+1/r_e(∠B)+1/r_e(∠C)) --> 1/(1/5+1/8+1/32)

Evaluating ... ...

r_i = 2.80701754385965

STEP 3: Convert Result to Output's Unit

2.80701754385965 Meter --> No Conversion Required

FINAL ANSWER

2.80701754385965 ≈ 2.807018 Meter <-- Inradius of Triangle

(Calculation completed in 00.020 seconds)

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Created by Venkata Sai Prasanna Aradhyula

Birla Institute of Technology & Science (BITS), Hyderabad

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< 7 Radius of Triangle Calculators

Circumradius of Triangle

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

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

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))

Inradius of Triangle by Heron's Formula

Go Inradius of Triangle = sqrt(((Semiperimeter of Triangle-Side C of Triangle)*(Semiperimeter of Triangle-Side B of Triangle)*(Semiperimeter of Triangle-Side A of Triangle))/Semiperimeter of Triangle)

Circumradius of Triangle given Three Exradii and Inradius

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

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

Go Circumradius of Triangle = Side A of Triangle/(2*sin(Angle A of Triangle))

Inradius of Triangle given Three Exradii Formula

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)
r_i = 1/(1/r_e(∠A)+1/r_e(∠B)+1/r_e(∠C))

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 Incircle of a Triangle ?

The Incircle or inscribed circle of a triangle is the largest circle contained in the triangle. It touches the three sides. The center of the incircle is a triangle center called the triangle's Incenter. Incenter is the point of intersection of all the 3 internal angular bisectors of the triangle

How to Calculate Inradius of Triangle given Three Exradii?

Inradius of Triangle given Three Exradii calculator uses 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) to calculate the Inradius of Triangle, The Inradius of Triangle given Three Exradii is defined as the length of the inradius of the incircle of the triangle, calculated using three exradii of the Triangle. Inradius of Triangle is denoted by r_i symbol.

How to calculate Inradius of Triangle given Three Exradii using this online calculator? To use this online calculator for Inradius of Triangle given Three Exradii, 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)) and hit the calculate button. Here is how the Inradius of Triangle given Three Exradii calculation can be explained with given input values -> 2.807018 = 1/(1/5+1/8+1/32).

FAQ

What is Inradius of Triangle given Three Exradii?

The Inradius of Triangle given Three Exradii is defined as the length of the inradius of the incircle of the triangle, calculated using three exradii of the Triangle and is represented as r_i = 1/(1/r_e(∠A)+1/r_e(∠B)+1/r_e(∠C)) or 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). 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.

How to calculate Inradius of Triangle given Three Exradii?

The Inradius of Triangle given Three Exradii is defined as the length of the inradius of the incircle of the triangle, calculated using three exradii of the Triangle is calculated using 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). To calculate Inradius of Triangle given Three Exradii, 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)). 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 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 Inradius of Triangle?

In this formula, Inradius of Triangle uses Exradius Opposite to ∠A of Triangle, Exradius Opposite to ∠B of Triangle & Exradius Opposite to ∠C of Triangle. We can use 2 other way(s) to calculate the same, which is/are as follows -

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))
Inradius of Triangle = sqrt(((Semiperimeter of Triangle-Side C of Triangle)*(Semiperimeter of Triangle-Side B of Triangle)*(Semiperimeter of Triangle-Side A of Triangle))/Semiperimeter of Triangle)

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