Consider the triangle ABC with incentre I, and the incircle touching the triangle at P, Q, R as shown in the diagram. As tangents drawn from a point are equal, AP=AQ, CP=CR and BQ=BR.
- In a triangle, the centroid divides the median in the ratio 2:1.
- If a is the side of an equilateral triangle, circumradius = $$ a/\sqrt{3}$$ and inradius = $$ = a/2\sqrt{3}$$.
- If a is the side of a triangle opposite to angle A, circumradius = $$\dfrac{a}{2\sin A}$$
- If a, b, and c are the sides of a right-angled triangle and c is the hypotenuse, then
Circumradius = $$\dfrac{c}{2}$$
Inradius = $$\dfrac{(a + b - c)}{2}$$
Area = $$s \times r$$, where $$s$$ is the semi-perimeter and $$r$$ is the in-radius.
