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