The bisector of the acute angle formed between the line $4x-3y+7=0$ and $3x-4y+14=0$ has the equation

Let $A$ be a fixed point $(0,6)$ and $B$ be a moving point $(2t,0).$ Let $M$ be the mid-point of $AB$ and the perpendicular bisector of $AB$ meets the $y-$axis at $C.$ The locus of the mid-point $P$ of $\mathrm{MC}$ is

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

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

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

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 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