Let (O) be inscribed inside triangle ABC, where AB,BC and CA are tangent to the circle (O) at D,E and F respectively. Sketch altitude CM BO where M is on the line BO. Let BD=4, DC=6 and the radius of the circle OD=OE=OF=2.

a) Find the length of CM and OM.

b) Prove that A is the right angle.

c) Find the perimeter of triangle ABC.

Note: No figure was provided by my teacher for this problem. Also, this question cannot be answered using cos,sin and tan.

I would greatly appreciate it if you help me solve this problem while showing all your work.