Question

The incentre of the triangle formed by the point $(0,0),(5,12),(16,12)$ is

• A. $(6,9)$
• B. $(7,9)$
• C. $(6,7)$
• D. $(9,7)$

Answer 1

The correct option is B $(7,9)$

Given,

$A(0,0),B(5,12),C(16,12)$

$AB=c=13$

$CA=b=20$

$BC=a=11$

$(x,y)=(\frac{a{x}_1+b{x}_1+c{x}_1}{a+b+c},\frac{a{y}_1+b{y}_1+c{y}_1}{a+b+c})$

$=(\frac{11\left(0\right)+20\left(5\right)+13\left(16\right)}{11+20+13},\frac{11\left(0\right)+20\left(12\right)+13\left(12\right)}{11+20+13})$

$=(\frac{0+100+208}{44},\frac{0+240+156}{44})$

$=(\frac{308}{44},\frac{396}{44})$

$\therefore (x,y)=(7,9)$