Difference between revisions of "Incircle"
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==Formulas== | ==Formulas== | ||
− | *The radius of an incircle of a triangle (the inradius) with sides <math>a,b,c</math> and area <math> | + | *The radius of an incircle of a triangle (the inradius) with sides <math>a,b,c</math> and area <math>A</math> is <math>\frac{2A}{a+b+c}</math> |
*The radius of an incircle of a right triangle (the inradius) with legs <math>a,b</math> and hypotenuse <math>c</math> is <math>r=\frac{ab}{a+b+c}=\frac{a+b-c}{2}</math>. | *The radius of an incircle of a right triangle (the inradius) with legs <math>a,b</math> and hypotenuse <math>c</math> is <math>r=\frac{ab}{a+b+c}=\frac{a+b-c}{2}</math>. | ||
− | *For any polygon with an incircle, <math> | + | *For any polygon with an incircle, <math>A=sr</math>, where <math>K</math> is the area, <math>s</math> is the semiperimeter, and <math>r</math> is the inradius. |
+ | |||
+ | *The formula for the semiperimeter is <math>s=\frac{a+b+c}{2}</math>. | ||
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+ | *And area of the triangle by Heron is <math>A^2=s(s-a)(s-b)(s-c)</math>. | ||
[[Category:Geometry]] | [[Category:Geometry]] |
Revision as of 08:33, 6 August 2017
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An incircle of a convex polygon is a circle which is inside the figure and tangent to each side. Every triangle and regular polygon has a unique incircle, but in general polygons with 4 or more sides (such as non- square rectangles) do not have an incircle. A quadrilateral that does have an incircle is called a Tangential Quadrilateral.
Formulas
- The radius of an incircle of a triangle (the inradius) with sides
and area
is
- The radius of an incircle of a right triangle (the inradius) with legs
and hypotenuse
is
.
- For any polygon with an incircle,
, where
is the area,
is the semiperimeter, and
is the inradius.
- The formula for the semiperimeter is
.
- And area of the triangle by Heron is
.