Incentre - Practice Questions & MCQ

Incentre

Incentre is the point of intersection of internal angle bisectors of triangle. And it is denoted by I.

The coordinates of Incentre (I) of triangle, whose vertices are A (x₁, y₁), B (x₂, y₂) and C(x₃, y₃), is given by 

\begin{equation}
\left(\frac{\mathrm{ax}_1+\mathrm{bx}_2+\mathrm{cx}_3}{\mathrm{a}+\mathrm{b}+\mathrm{c}}, \frac{\mathrm{ay}_1+\mathrm{by}_2+\mathrm{cy}_3}{\mathrm{a}+\mathrm{b}+\mathrm{c}}\right)
\end{equation}

Where, a, b and c are the length of side BC, CA and AB respectively.

NOTE:

If ΔABC is equilateral triangle, then a = b = c

Coordinates of Incentre (I) = Coordinates of Centroid (G) = 

\begin{equation}
\left(\frac{\mathrm{x}_1+\mathrm{x}_2+\mathrm{x}_3}{3}, \frac{\mathrm{y}_1+\mathrm{y}_2+\mathrm{y}_3}{3}\right)
\end{equation}