Triangle and its Types

The sides of a triangle are $6 \mathrm{cm}$, $11 \mathrm{cm}$ and $15 \mathrm{cm}$.  The radius of its incentre is?

$\mathrm{PQR}$ is a right-angled triangle, right-angled at $\mathrm{Q}$. A circle is inscribed in it. The lengths of the two sides of triangle containing the right angle are $6 \mathrm{cm}$ and $8 \mathrm{cm}$ respectively. Find the radius of the incircle in $\mathrm{cm}$.

The incentre of the triangle with vertices $\left(1, \sqrt{3}\right), \left(0, 0\right) \& \left(2, 0\right)$ is

$△ABC$ is a right angled triangle. If $CD=k \mathrm{cm}$ then find $k$.

If the altitude of a triangle is $k \mathrm{cm}$, its area is $120 {\mathrm{cm}}^2$ and its base is $6 \mathrm{cm}$ then find $k$.

If the altitude of an equilateral triangle when its equal sides are given as $10 \mathrm{cm}$ is $k\sqrt{3} \mathrm{cm}$ then find $k$.

Every triangle has $4$ altitudes, one from each vertex.

The $3$ medians divide the triangle into $8$ smaller triangles of equal area.

Every triangle has$3$ medians.

The orthocenter is located inside the triangle in _____ triangle. (Acute/Right) 

Given: $BX$ is the altitude, $\angle BAX=40°$. If $\angle 1=k°$ then find $k$.

Given: $AX$ is the altitude, $\angle CAB\cong \angle B, \angle C=50°$. If $\angle B$ is $k°$ then find $k$

 $G$ is the centroid of triangle $ABC$ and $BF=10$. If the length of $FA$ is $x$ then find $x$.

The centroid of a triangle is the point at which its three medians intersect.

In $△ABC,$ the median $AD, BE$ and $CF$ passes through the point $G$. If $AD=7.5 \mathrm{cm},$ then find $GD$ (in $\mathrm{cm}$) (correct up to one decimal place)

In $△ABC,$ the median $AD, BE$ and $CF$ passes through the point $G$. If $GF=4 \mathrm{cm}$ then, find $GC$ (in $\mathrm{cm}$).

Town A, Town B and Town C are connected by three highways. The government wants to set up a police station to check crimes on the highway. What is the best location for the police station so that it is equidistant and easier to access from the highway?

Which point of concurrency is represented by O?

If O is the circumcentre of the triangle then

Identify the circum circle in the figure given above