Softball solution

If Jan divides the diamond into quarters she gets this right-angled triangle:

12.93m is half of the distance of 25.86 metres between home plate and second base.

So n² = 12.93²+12.93² (Pythagoras)

So n² = 334.37 (Squaring and adding)

So n = 18.29 m (Finding the square root)

If Jan creates a rope that is 2 x 18.29m long (36.58m) she can mark the exact centre of it. If she fixes the ends of the rope to home and second plate she can pull on the middle of the rope until it is tight.

The centre mark will be the place of the first or third base and the angle must be a right angle.