Inradius of Isosceles Triangle Calculator

✖Base of Isosceles Triangle is the third and unequal side of the Isosceles Triangle.ⓘ Base of Isosceles Triangle [S_Base]			+10% -10%
✖The Legs of Isosceles Triangle are the two equal sides of the Isosceles Triangle.ⓘ Legs of Isosceles Triangle [S_Legs]			+10% -10%

✖The Inradius of Isosceles Triangle is defined as the radius of the circle inscribed inside the Isosceles Triangle.ⓘ Inradius of Isosceles Triangle [r_i]

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Formula

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Inradius of Isosceles Triangle

Formula

`"r"_{"i"} = "S"_{"Base"}/2*sqrt((2*"S"_{"Legs"}-"S"_{"Base"})/(2*"S"_{"Legs"}+"S"_{"Base"}))`

Example

`"2.12132m"="6m"/2*sqrt((2*"9m"-"6m")/(2*"9m"+"6m"))`

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Inradius of Isosceles Triangle Solution

STEP 0: Pre-Calculation Summary

Formula Used

Inradius of Isosceles Triangle = Base of Isosceles Triangle/2*sqrt((2*Legs of Isosceles Triangle-Base of Isosceles Triangle)/(2*Legs of Isosceles Triangle+Base of Isosceles Triangle))
r_i = S_Base/2*sqrt((2*S_Legs-S_Base)/(2*S_Legs+S_Base))
This formula uses 1 Functions, 3 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

Inradius of Isosceles Triangle - (Measured in Meter) - The Inradius of Isosceles Triangle is defined as the radius of the circle inscribed inside the Isosceles Triangle.
Base of Isosceles Triangle - (Measured in Meter) - Base of Isosceles Triangle is the third and unequal side of the Isosceles Triangle.
Legs of Isosceles Triangle - (Measured in Meter) - The Legs of Isosceles Triangle are the two equal sides of the Isosceles Triangle.

STEP 1: Convert Input(s) to Base Unit

Base of Isosceles Triangle: 6 Meter --> 6 Meter No Conversion Required
Legs of Isosceles Triangle: 9 Meter --> 9 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

r_i = S_Base/2*sqrt((2*S_Legs-S_Base)/(2*S_Legs+S_Base)) --> 6/2*sqrt((2*9-6)/(2*9+6))

Evaluating ... ...

r_i = 2.12132034355964

STEP 3: Convert Result to Output's Unit

2.12132034355964 Meter --> No Conversion Required

FINAL ANSWER

2.12132034355964 ≈ 2.12132 Meter <-- Inradius of Isosceles Triangle

(Calculation completed in 00.020 seconds)

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Home » Math » Geometry » 2D Geometry » Triangle » Isosceles Triangle » Radius of Isosceles Triangle » Inradius of Isosceles Triangle

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< 6 Radius of Isosceles Triangle Calculators

Inradius of Isosceles Triangle given Legs and Height

Go Inradius of Isosceles Triangle = (Height of Isosceles Triangle*sqrt(Legs of Isosceles Triangle^2-Height of Isosceles Triangle^2))/(Legs of Isosceles Triangle+sqrt(Legs of Isosceles Triangle^2-Height of Isosceles Triangle^2))

Inradius of Isosceles Triangle

Go Inradius of Isosceles Triangle = Base of Isosceles Triangle/2*sqrt((2*Legs of Isosceles Triangle-Base of Isosceles Triangle)/(2*Legs of Isosceles Triangle+Base of Isosceles Triangle))

Inradius of Isosceles Triangle given Legs and Base Angle

Go Inradius of Isosceles Triangle = Legs of Isosceles Triangle*cos(Base Angles of Isosceles Triangle)*tan(Base Angles of Isosceles Triangle/2)

Circumradius of Isosceles Triangle

Go Inradius of Isosceles Triangle = Legs of Isosceles Triangle^2/sqrt(4*Legs of Isosceles Triangle^2-Base of Isosceles Triangle^2)

Inradius of Isosceles Triangle given Base and Base Angle

Go Inradius of Isosceles Triangle = Base of Isosceles Triangle/2*tan(Base Angles of Isosceles Triangle/2)

Circumradius of Isosceles Triangle given Legs and Height

Go Circumradius of Isosceles Triangle = Legs of Isosceles Triangle^2/(2*Height of Isosceles Triangle)

< 4 Radius of Isosceles Triangle Calculators

Inradius of Isosceles Triangle given Base and Height

Go Inradius of Isosceles Triangle = (Base of Isosceles Triangle*Height of Isosceles Triangle)/(Base of Isosceles Triangle+sqrt(4*Height of Isosceles Triangle^2+Base of Isosceles Triangle^2))

Inradius of Isosceles Triangle

Go Inradius of Isosceles Triangle = Base of Isosceles Triangle/2*sqrt((2*Legs of Isosceles Triangle-Base of Isosceles Triangle)/(2*Legs of Isosceles Triangle+Base of Isosceles Triangle))

Inradius of Isosceles Triangle given Legs and Base Angle

Go Inradius of Isosceles Triangle = Legs of Isosceles Triangle*cos(Base Angles of Isosceles Triangle)*tan(Base Angles of Isosceles Triangle/2)

Circumradius of Isosceles Triangle

Go Inradius of Isosceles Triangle = Legs of Isosceles Triangle^2/sqrt(4*Legs of Isosceles Triangle^2-Base of Isosceles Triangle^2)

Inradius of Isosceles Triangle Formula

What is an Isosceles Triangle?

An Isosceles Triangle is a triangle with two sides of equal length, which are called legs. The third side of the triangle is called the base. Vertex angle is the angle between the legs and the angles with the base as one of their sides are called the base angles.

What is inscribed circle and how its radius calculated for an isosceles triangle ?

In geometry, the incircle or inscribed circle of a triangle is the largest circle contained in the triangle; it touches (is tangent to) the three sides. Its centre is known as incentre and its radius is known as inradius. It is calculated by the formula is r = b √ ((2a-b)/ (2a+b)) / 2 where r is the radius of the inscribed circle and a, b are the sides of an isosceles triangle.

How to Calculate Inradius of Isosceles Triangle?

Inradius of Isosceles Triangle calculator uses Inradius of Isosceles Triangle = Base of Isosceles Triangle/2*sqrt((2*Legs of Isosceles Triangle-Base of Isosceles Triangle)/(2*Legs of Isosceles Triangle+Base of Isosceles Triangle)) to calculate the Inradius of Isosceles Triangle, Inradius of Isosceles Triangle formula is defined as the length of the radius of the circle which is the largest circle inside the triangle, it touches (is tangent to) the three sides. Inradius of Isosceles Triangle is denoted by r_i symbol.

How to calculate Inradius of Isosceles Triangle using this online calculator? To use this online calculator for Inradius of Isosceles Triangle, enter Base of Isosceles Triangle (S_Base) & Legs of Isosceles Triangle (S_Legs) and hit the calculate button. Here is how the Inradius of Isosceles Triangle calculation can be explained with given input values -> 2.12132 = 6/2*sqrt((2*9-6)/(2*9+6)).

FAQ

What is Inradius of Isosceles Triangle?

Inradius of Isosceles Triangle formula is defined as the length of the radius of the circle which is the largest circle inside the triangle, it touches (is tangent to) the three sides and is represented as r_i = S_Base/2*sqrt((2*S_Legs-S_Base)/(2*S_Legs+S_Base)) or Inradius of Isosceles Triangle = Base of Isosceles Triangle/2*sqrt((2*Legs of Isosceles Triangle-Base of Isosceles Triangle)/(2*Legs of Isosceles Triangle+Base of Isosceles Triangle)). Base of Isosceles Triangle is the third and unequal side of the Isosceles Triangle & The Legs of Isosceles Triangle are the two equal sides of the Isosceles Triangle.

How to calculate Inradius of Isosceles Triangle?

Inradius of Isosceles Triangle formula is defined as the length of the radius of the circle which is the largest circle inside the triangle, it touches (is tangent to) the three sides is calculated using Inradius of Isosceles Triangle = Base of Isosceles Triangle/2*sqrt((2*Legs of Isosceles Triangle-Base of Isosceles Triangle)/(2*Legs of Isosceles Triangle+Base of Isosceles Triangle)). To calculate Inradius of Isosceles Triangle, you need Base of Isosceles Triangle (S_Base) & Legs of Isosceles Triangle (S_Legs). With our tool, you need to enter the respective value for Base of Isosceles Triangle & Legs of Isosceles 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 Isosceles Triangle?

In this formula, Inradius of Isosceles Triangle uses Base of Isosceles Triangle & Legs of Isosceles Triangle. We can use 7 other way(s) to calculate the same, which is/are as follows -

Inradius of Isosceles Triangle = Legs of Isosceles Triangle^2/sqrt(4*Legs of Isosceles Triangle^2-Base of Isosceles Triangle^2)
Inradius of Isosceles Triangle = Legs of Isosceles Triangle*cos(Base Angles of Isosceles Triangle)*tan(Base Angles of Isosceles Triangle/2)
Inradius of Isosceles Triangle = (Height of Isosceles Triangle*sqrt(Legs of Isosceles Triangle^2-Height of Isosceles Triangle^2))/(Legs of Isosceles Triangle+sqrt(Legs of Isosceles Triangle^2-Height of Isosceles Triangle^2))
Inradius of Isosceles Triangle = Base of Isosceles Triangle/2*tan(Base Angles of Isosceles Triangle/2)
Inradius of Isosceles Triangle = Legs of Isosceles Triangle^2/sqrt(4*Legs of Isosceles Triangle^2-Base of Isosceles Triangle^2)
Inradius of Isosceles Triangle = Legs of Isosceles Triangle*cos(Base Angles of Isosceles Triangle)*tan(Base Angles of Isosceles Triangle/2)
Inradius of Isosceles Triangle = (Base of Isosceles Triangle*Height of Isosceles Triangle)/(Base of Isosceles Triangle+sqrt(4*Height of Isosceles Triangle^2+Base of Isosceles Triangle^2))

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