let AB = b be the base of triangle ABC and h = height from C to AB ...
area of triangle ABC = (1/2)bh = r
since AD = (1/4)b
area of triangle ADC = (1/2)(1/4)bh = (1/4)(1/2)bh = (1/4)r
AD/DB=1/3, so think of line AB as being divided into 4 equal segments, and that each of the three points dividing the line segments on AB have a straight line connecting to point C, creating 4 equal triangles within the triangle ABC, ADC being one of those
therefore, triangle ADC=(1/4)r