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Circumradius of Triangle given Three Exradii and Inradius Formula

GoCircumradius of Triangle given One Side and its Opposite Angle Formula

GoCircumradius of Triangle Formula

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Circumradius of Triangle is the radius of a circumcircle touching each of the vertices of the Triangle. Check FAQs

r c = \frac{r e(∠A) + r e(∠B) + r e(∠C) - r i}{4}

r_c - Circumradius of Triangle?r_e(∠A) - Exradius Opposite to ∠A of Triangle?r_e(∠B) - Exradius Opposite to ∠B of Triangle?r_e(∠C) - Exradius Opposite to ∠C of Triangle?r_i - Inradius of Triangle?

Circumradius of Triangle given Three Exradii and Inradius Example

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Here is how the Circumradius of Triangle given Three Exradii and Inradius equation looks like with Units.

Here is how the Circumradius of Triangle given Three Exradii and Inradius equation looks like.

10.5 = \frac{5 + 8 + 32 - 3}{4}

10.5m = \frac{5m + 8m + 32m - 3m}{4}

10.5 = \frac{5 + 8 + 32 - 3}{4}

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Circumradius of Triangle given Three Exradii and Inradius Solution

Follow our step by step solution on how to calculate Circumradius of Triangle given Three Exradii and Inradius?

FIRST Step Consider the formula

r c = \frac{r e(∠A) + r e(∠B) + r e(∠C) - r i}{4}

Next Step Substitute values of Variables

∴

r c = \frac{5m + 8m + 32m - 3m}{4}

Next Step Prepare to Evaluate

∴

r c = \frac{5 + 8 + 32 - 3}{4}

LAST Step Evaluate

∴

r c = 10.5m

Circumradius of Triangle given Three Exradii and Inradius Formula Elements

Variables

Circumradius of Triangle

Circumradius of Triangle is the radius of a circumcircle touching each of the vertices of the Triangle.

Symbol: r_c

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Circumradius of Triangle

Exradius Opposite to ∠A 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.

Symbol: r_e(∠A)

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Exradius Opposite to ∠A of Triangle

Exradius Opposite to ∠B of Triangle

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.

Symbol: r_e(∠B)

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Exradius Opposite to ∠B of Triangle

Exradius Opposite to ∠C of Triangle

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.

Symbol: r_e(∠C)

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Exradius Opposite to ∠C of Triangle

Inradius of Triangle

Inradius of Triangle is defined as the radius of the circle which is inscribed inside the Triangle.

Symbol: r_i

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Inradius of Triangle

Other Formulas to find Circumradius of Triangle

Go Circumradius of Triangle given One Side and its Opposite Angle

r c = \frac{S a}{2 \cdot \sin (∠A)}

Go Circumradius of Triangle

r c = \frac{S a \cdot S b \cdot S c}{\sqrt{(S a + S b + S c) \cdot (S b - S a + S c) \cdot (S a - S b + S c) \cdot (S a + S b - S c)}}

Other formulas in Radius of Triangle category

Go Inradius of Triangle given Three Exradii

r i = \frac{1}{\frac{1}{r e(∠A)} + \frac{1}{r e(∠B)} + \frac{1}{r e(∠C)}}

Go Inradius of Triangle

r i = \frac{\sqrt{(S a + S b + S c) \cdot (S b + S c - S a) \cdot (S a - S b + S c) \cdot (S a + S b - S c)}}{2 \cdot (S a + S b + S c)}

Go Exradius Opposite to Angle A of Triangle

r e(∠A) = \sqrt{\frac{(\frac{S a + S b + S c}{2}) \cdot (\frac{S a - S b + S c}{2}) \cdot (\frac{S a + S b - S c}{2})}{\frac{S b + S c - S a}{2}}}

Go Inradius of Triangle by Heron's Formula

r i = \sqrt{\frac{(s - S c) \cdot (s - S b) \cdot (s - S a)}{s}}

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

Circumradius of Triangle given Three Exradii and Inradius evaluator 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 evaluate 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 evaluate Circumradius of Triangle given Three Exradii and Inradius using this online evaluator? To use this online evaluator 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.

FAQs on Circumradius of Triangle given Three Exradii and Inradius

What is the formula to find Circumradius of Triangle given Three Exradii and Inradius?

The formula of Circumradius of Triangle given Three Exradii and Inradius is expressed as 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. Here is an example- 10.5 = (5+8+32-3)/4.

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

With 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) we can find Circumradius of Triangle given Three Exradii and Inradius using the formula - 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.

What are the other ways to Calculate Circumradius of Triangle?

Here are the different ways to Calculate Circumradius of Triangle-

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))

Can the Circumradius of Triangle given Three Exradii and Inradius be negative?

No, the Circumradius of Triangle given Three Exradii and Inradius, measured in Length cannot be negative.

Which unit is used to measure Circumradius of Triangle given Three Exradii and Inradius?

Circumradius of Triangle given Three Exradii and Inradius is usually measured using the Meter[m] for Length. Millimeter[m], Kilometer[m], Decimeter[m] are the few other units in which Circumradius of Triangle given Three Exradii and Inradius can be measured.

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Circumradius of Triangle given Three Exradii and Inradius Formula

​GoCircumradius of Triangle given One Side and its Opposite Angle Formula

​GoCircumradius of Triangle Formula

Circumradius of Triangle given Three Exradii and Inradius Example

Circumradius of Triangle given Three Exradii and Inradius Solution

Circumradius of Triangle given Three Exradii and Inradius Formula Elements

Other Formulas to find Circumradius of Triangle

Other formulas in Radius of Triangle category

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

FAQs on Circumradius of Triangle given Three Exradii and Inradius

Variable Name

GoCircumradius of Triangle given One Side and its Opposite Angle Formula

GoCircumradius of Triangle Formula