Question

In square ABCD , diagonals meet at O. P is a point on BC such that AB is equal to BP .find out angle POC,angle BDC and angle BOP.

Answer 1

a square is a cyclic quadrilateral and AC BD are dia.
AOB=BOC=COD=DOA=90 deg
OBC is a Rt.angled triangle with OBC=OCB=45 deg.
with OP=BP equal,it forms isosceles triangle with OBP=45 deg
and other two angles namely BOP=BPO=135/2=67.5 deg.
POC =BOC-BOP=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).