see the light

This is proof that every triangle on this world is isosceles ofcourse there is mistake. Find it and than you can tell me what do you think.


OP = OP
AP = BP (=1/2 AB)
Angles APO and BPO are also equal(=90)
That means that triangle APO is homologous to BPO
That means that OA=OB.

OC=OC
angles ACP and BCP are also equal, and also QOB and ROA
That means that triangle ORC is homologous to OQC
That means that CR=CQ

Now:
OA=OB
OR=OQ
Angle is 90
That means that triangle AOR is homologous to BOQ
That means that AR is homologous to BQ

So that all means that AC=BC so that means that all triangles are isosceles
which is of course wrong.