The incenter and centroid of the triangle, whose vertices are $A \equiv(0,3,0), B \equiv(0,0,4)$, and $C \equiv(0,3,4)$, are respectively given by

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$A \equiv(0,3,0), B \equiv(0,0,4)$, and $C \equiv(0,3,4)$ $a=B C=3$ $b=C A=4$ $c=A B=5$. $\begin{aligned} & 	ext { Now, Incentre } \equiv\left(\frac{a x_1+b x_2+c x_3}{a+b+c}, \frac{a y_1+b y_2+c y_3}{a+b+c}, \frac{a z_1+b z_2+c z_3}{a+b+c}ight) \ & \equiv\left(\frac{3 	imes 0+4 	imes 0+5 	imes 0}{3+4+5}, \frac{3 	imes 3+4 	imes 0+5 	imes 3}{3+4+5}, \frac{3 	imes 0+4 	imes 4+5 	imes 4}{3+4+5}ight) \ & \equiv(0,2,3) \ & 	ext { and centroid } \equiv\left(\frac{x_1+x_2+x_3}{3}, \frac{y_1+y_2+y_3}{3}, \frac{z_1+z_2+z_3}{3}ight)\end{aligned}$ $\begin{aligned} & \equiv\left(\frac{0+0+0}{3}, \frac{3+0+3}{3}, \frac{0+4+4}{3}ight) \ & \equiv\left(0,2, \frac{8}{3}ight)\end{aligned}$

The incenter and centroid of the triangle, whose vertices are $A \equiv(0,3,0), B \equiv(0,0,4)$, and $C…

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