A circle touches side $BC$ at point $P$ of $\triangle ABC$, from outside of the triangle. Further extended lines $AC$ and $AB$ are tangents to the circle at $N$ and $M$ respectively. Prove that: \[ AM = \frac{1}{2} (\text{Perimeter of } \triangle ABC) \]
Find the co-ordinates of point P where P is the midpoint of a line segment AB with A($-4$, 2) and B(6, 2).
In $\triangle PQR$, seg $PM$ is a median. Angle bisectors of $\angle PMQ$ and $\angle PMR$ intersect sides $PQ$ and $PR$ in points $X$ and $Y$ respectively. Prove that $XY \parallel QR$.
In the given figure, points G, D, E, F are points on a circle with centre C. If $\angle ECF = 70^\circ$ and $m(\text{arc } DGF) = 200^\circ$, find: (i) $m(\text{arc } DE)$ (ii) $m(\text{arc } DEF)$
In trapezium $ABCD$, side $AB \parallel PQ \parallel DC$. If $AP = 3$, $PD = 12$, and $QC = 14$, find $BQ$.
In the figure below, $\angle L = 35^\circ$. Find: (i) $m(\text{arc } MN)$ (ii) $m(\text{arc } MLN)$
