Triangles

Perimeter of triangle

$$P = a+b+c$$

Find It is known that:

Calculate 'P'

Semiperimeter of triangle

$$p = \frac{a+b+c}{2}$$

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Calculate 'p'

Cosine rule

$$c^{2} = a^{2}+b^{2}-2\cdot a\cdot b\cdot cos(\alpha)$$

α - the angle between a and b

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Calculate 'c'

Law of sines (sine rule)

$$\frac{a}{sin(A)} = \frac{b}{sin(B)}$$

A - opposite angle of side a
B - opposite angle of side b

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Calculate 'a'

Law of sines (sine rule)

$$\frac{a}{sin(A)} = 2\cdot R$$

A - opposite angle of side a
R - circumradius

Find It is known that:

Calculate 'a'

Angle bisector theorem

$$\frac{m}{n} = \frac{b}{c}$$

b, c - triangle sides
m, n - lengths of the two segments that a triangle's side is divided into by a bisector

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Calculate 'm'

Bisector (bisectrix) of triangle

$$l = \sqrt {b\cdot c-m\cdot n}$$

l - length of bisector
b, c - triangle sides
m, n - lengths of the two segments that a triangle's side is divided into by a bisector

Find It is known that:

Calculate 'l'

Length of triangle median

$$m_{a} = \frac{1}{2}\cdot \sqrt {2\cdot (b^{2}+c^{2})-a^{2}}$$

m_a - length of median drawn to the side a
a, b, c - triangle sides

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Calculate 'm_a'

Inradius of triangle

$$r = \frac{S}{p}$$

r - inradius
S - triangle area
p - half perimeter (semiperimeter) of triangle

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Calculate 'r'

Circumradius of a triangle

$$R = \frac{a\cdot b\cdot c}{4}\cdot S$$

R - circumradius
a, b, c - triangle sides
S - triangle area

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Calculate 'R'

Pythagorean theorem

$$c^{2} = a^{2}+b^{2}$$

c - hypotenuse
a,b - triangle sides

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Calculate 'c'

Inradius of right (angled) triangle

$$r = \frac{a+b-c}{2}$$

r - the inradius
c - hypotenuse
a,b - triangle sides

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Calculate 'r'

Circumradius of a right (angled) triangle

$$R = \frac{c}{2}$$

R - circumradius
c - hypotenuse

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Calculate 'R'

Circumradius of a equilateral triangle

$$R = \frac{a\cdot \sqrt {3}}{3}$$

R - circumradius
a - side

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Calculate 'R'

Inradius of a equilateral triangle

$$r = \frac{a\cdot \sqrt {3}}{6}$$

r - the inradius
a - side

Find It is known that:

Calculate 'r'