F.3 Maths~Deductive Geometry

Given a triangle with sides that have length a, b, and c.


圖片參考：http://courses.ncssm.edu/goebel/probsolv/Image340.gif


The semiperimeter s is half the sum of the lengths of the sides.
圖片參考：http://courses.ncssm.edu/goebel/probsolv/Image341.gif

The area of the triangle, K can be found by the following formulae:


圖片參考：http://courses.ncssm.edu/goebel/probsolv/Image342.gif
, where b could be any side and h the altitude to that side.

圖片參考：http://courses.ncssm.edu/goebel/probsolv/Image343.gif
, where a and b are any two sides and C the included angle.

圖片參考：http://courses.ncssm.edu/goebel/probsolv/Image344.gif
, where s is the semiperimeter.
To see the derivations of any of these formulas click on the formula.
In any triangle, a circle can be inscribe in it. This circle will have center at the incenter (the point of concurency of the angle-bisectors) and the radius of this circle is related to the area of the circle and the lengths of the sides by the following formula:


圖片參考：http://courses.ncssm.edu/goebel/probsolv/Image345.gif
, where K is the area of the triangle and s is the semiperimeter.


圖片參考：http://courses.ncssm.edu/goebel/probsolv/Image346.gif