Incentre

Q. If the vertices of $△ABC$ are $A=(3,-5),B=(-3,3)$ and $C=(-1,-2)$ and internal angle bisector through $A$ cuts the side $BC$ at $D,$ then the length of $AD$ is

1. $\frac{7}{3}\sqrt{2}$ units
2. $\frac{14}{3}\sqrt{2}$ units
3. $\frac{3}{7}\sqrt{2}$ units
4. $\frac{3}{14}\sqrt{2}$ units

Q.

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

1. (7, 9)

2. (9, 7)

3. (-9, 7)

4. (-7, 9)

Q. The incentre of the triangle whose vertices are $(1,\sqrt{3}),(0,0)$ and $(2,0)$ is

1. $(1,\frac{\sqrt{3}}{2})$
2. $(\frac{2}{3},\frac{1}{\sqrt{3}})$
3. $(\frac{2}{3},\frac{\sqrt{3}}{2})$
4. $(1,\frac{1}{\sqrt{3}})$

Q. The incentre of the triangle whose vertices are $(1,\sqrt{3}),(0,0)$ and $(2,0)$ is

1. $(1,\frac{\sqrt{3}}{2})$
2. $(\frac{2}{3},\frac{1}{\sqrt{3}})$
3. $(\frac{2}{3},\frac{\sqrt{3}}{2})$
4. $(1,\frac{1}{\sqrt{3}})$

Q. The incentre of the triangle whose vertices are $(1,\sqrt{3}),(0,0)$ and $(2,0)$ is

1. $(1,\frac{\sqrt{3}}{2})$
2. $(\frac{2}{3},\frac{1}{\sqrt{3}})$
3. $(\frac{2}{3},\frac{\sqrt{3}}{2})$
4. $(1,\frac{1}{\sqrt{3}})$