Question

In a square ABCD, diagonal AC and BD bisect each other at O. P is a point on side BC such that BP is equal to OB then find angle COP.​

Answer 1

#BAL

given: ABCD is a square and OB = BP

in the triangle OBP;

∠BOP = ∠OPB

∠OBP = 90/2 = 45 deg [by the symmetry]

∠BOP = (180-45) / 2 = 135 / 2 = 67.5 deg

∠BOC = 90 deg [diagonals of a square bisect at right angle]

∠POC = 90 - 67.5 = 22.5 deg

again BDC is an isosceles triangle with BCD=90 deg.

and BDC=DBC=45 deg.=2*22.5(POC).