The solution 1 because om = on om on is perpendicular to oa ob and intersects with point p, respectively.

So op is the bisector of angle o (defined by the bisector of angle)

Solution 2 because om=on op=op angle omp= angle onp=90 degrees.

So triangle omp is equal to triangle onp(HL)

So angle mop= angle nop

So OP is the bisector of ∠AOB