Question

Find the ratio of x coordinate to y coordinate of incentre of a triangle whose midpoint of its sides are $(0,1),(1,1),(1,0)$

Answer 1

$\therefore$Coordinates of $A(2,0)$

Coordinates of $B(0,2)$

Coordinates of $C(0,O)$

$AB=c=2\sqrt{2}AC=b=2\sqrt{2}BC=a=2\sqrt{2}Asthesidesareequalsoequilateraltriangle\therefore Incentreis(\frac{2+0+0}{3},\frac{0+2+0}{3})=(\frac{2}{3},\frac{2}{3})\therefore Ratio=1$