ABC is a triangle right angled at C.

[question] Question. ABC is a triangle right angled at C. A line through the mid-point M of hypotenuse AB and parallel to BC intersects AC at D. Show that (i) D is the mid-point of AC (ii) $\mathrm{MD} \perp \mathrm{AC}$ (iii) $\mathrm{CM}=\mathrm{MA}=\frac{1}{2} \mathrm{AB}$ [/question] [solution] Solution: (i) $\ln \triangle \mathrm{ABC}$, It is given that $M$ is the mid-point of $A B$ and $M D \| B C$. Therefore, $D$ is the mid-point of $A C$. (Converse of mid-point theorem) (ii) $A s D M \| ...