Prove that the quadrilateral formed by angle bisectors of a cyclic quadrilateral are also cyclic
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DAR=BAR
ABR=CBR
ADP=PDC
PCD=PCB
DAB+DCB=180
So PCB=PCD=90-x
Similarly, RBC=90-y
In Tri DPC
DPC= 180-y-90+x=90+x-y
In Tri ARB
ARB= 180-x-90+y = 90+y-x
since ARB+DPC=180
Quad. SPQR is cyclic
(sum of opp. angles of cyclic quad. is 180)
ABR=CBR
ADP=PDC
PCD=PCB
DAB+DCB=180
So PCB=PCD=90-x
Similarly, RBC=90-y
In Tri DPC
DPC= 180-y-90+x=90+x-y
In Tri ARB
ARB= 180-x-90+y = 90+y-x
since ARB+DPC=180
Quad. SPQR is cyclic
(sum of opp. angles of cyclic quad. is 180)
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