Question

The incenter of a triangle is given by:

• A. $(x,y)\equiv (\frac{a{x}_1+b{x}_2+c{x}_3}{a+b+c},\frac{a{y}_1+b{y}_2+c{y}_3}{a+b+c})$
• B. $(x,y)\equiv (a{x}_1+b{x}_2+c{x}_3,a{y}_1+b{y}_2+c{y}_3)$
• C. $(x,y)\equiv (\frac{x_1+x_2+x_3}{a+b+c},\frac{y_1+y_2+y_3}{a+b+c})$
• D. $(x,y)\equiv (\frac{a+b+c}{x_1+x_2+x_3},\frac{a+b+c}{y_1+y_2+y_3})$

Answer 1

The correct option is A

$(x,y)\equiv (\frac{a{x}_1+b{x}_2+c{x}_3}{a+b+c},\frac{a{y}_1+b{y}_2+c{y}_3}{a+b+c})$

The incentre is the point of intersection of angle bisectors of the triangle.

The incenter of a triangle is given by,

$(x,y)\equiv (\frac{a{x}_1+b{x}_2+c{x}_3}{a+b+c},\frac{a{y}_1+b{y}_2+c{y}_3}{a+b+c})$

where, $(x_1,y_1),(x_2,y_2),(x_3,y_3)$ are coordinates of the triangle, and a, b, c are the lengths of 3 sides.