State the converse of angle bisector theorem.

In $△ABC$, it is given that $\frac{BD}{DC}=\frac{AB}{AC}, \angle B=70°, \angle C=50°.$ Find $\angle BAD$ in degrees.

In the given figure, $AD$ is the bisector of $\angle BAC$. If $AB=10cm, AC=6cm$ and $BC=12cm$. Find $BD$.

In $△PQR$, the bisector of $\angle P$ intersects $QR$ in $M$. If $PQ=10, PR=12, QM=8$ then $QR=$ _____.

In the given fig.$AM\perp BC$ and $AN$ is the bisector of $\angle A$. If $\angle B=65°$ and $\angle C=33°$, then the value of $\angle MAN$ will be

Let $a, b, c$ be the side-length of a triangle and $l, m, n$ be the lengths of its medians. Put $K=\frac{l+m+n}{a+b+c}$ Then, as $a, b, c$ vary, $K$ can assume every value in the interval

If all the $3$ vertices of an isosceles right angle triangle be integral points and length of base is also an integer, then which of the point is never a rational point (A point $P(x,y)$ is integral point if both `x` and `y` are integers and point is rational, if both `x` and `y` are rational).