Patroll in the garden

A triangular garden has a path on the perimeter, and three other paths joining the bandstand P to each vertices.
The sides are 800, 850 and 900 m.
Three guards patroll in this garden. Each on a different circuit, always the same, through one side of the garden and two of the inner paths.
They walk at the same constant speed, and meet at eaxh round at the stand.

Where is the stand ? Solution

What is their speed if each round lasts 1/2 h ? Solution
Details

 

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