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) MD ⊥ AC

(iii) CM = MA = \frac { 1 }{ 2 } AB

(i) D is the mid-point of AC

(ii) MD ⊥ AC

(iii) CM = MA = \frac { 1 }{ 2 } AB