If a point P divides the line segment joining A (position vector a) and B (position vector b) in the ratio m:n, then: Internal division: p = $\frac{m**b** + n**a**}{(m+n)}$. External division: p = $\frac{m**b** - n**a**}{(m-n)}$. Special cases: Midpoint (m=n=1): p = $\frac{**a**+**b**}{2}$. Centroid of triangle with vertices a, b, c: g = $\frac{**a**+**b**+**c**}{3}$. Incenter: r = $\frac{a·**A** + b·**B** + c·**C**}{(a+b+c)}$ where a, b, c are side lengths opposite to vertices A, B, C.