Two things you need to know about this proof:
A "midsegment" of a triangle is a segment that connects the midpoints of two
sides of a triangle.
A midsegment of a triangle is parallel to the third side and is half the length
of the third side.
∥ΔΔߛ ߜθθθθθσΔΔΔ⌀⎣ ⎦ ᑎ≤≥≦≧≅∠Δ
Here's an outline for the proof, you'll have to write a two-column
proof yourself.
Two segments marked the same above are given equal by definition
of median and midpoint.
MI is a midsegment of ΔRDT, so 
and RD ∥ MI and so OD ∥ MI, and since AO = OM, AD = DI.
So we now know that OD is a midline of ΔMAI.
So these three segments DA, DI, and IT are all equal:
DA = DI = IT, So it's immediate that 
.
Since we now know that OD is a midline of ΔMAI, OD is half
of MI, and MI is half of RD, so 
,
because half of a half is a fourth.
Now go write up the two-column proof. If you have any
questions about the above, ask them in the thank-you note
and I'll get back to you. BTW I don't charge any money,
I'm a retired prof and just do this for fun.
Edwin
