1。 If triangle BCP rotates 90 degrees clockwise around A to form triangle B' C' P', then B' coincides with C, and C' coincides with D.

It is easy to get the three-point * * line of OP=OP' and P P' C, so PP' = BP+CP.

The triangle OPP'' is an isosceles right triangle, so PP'=√2OP, that is, BP+CP=√2OP.

2。 The same proof idea (rotation) can be given as |BP-CP|=√2OP.

I hope it helps you.