Prove that the quadrilateral formed by angle bisector of a cyclic quadrilateral is also cyclic

Prove that the quadrilateral formed by angle bisector of a cyclic quad

1.	Prove that the quadrilateral formed by angle bisector of a cyclic quadrilateral is also cyclic
Answer» Consider a quad. Abcd with angle bisectors of a,b,c and d meet at p,q,r and s forming a quad.Now take the angles and a=1 + 1 where 1 is an angle similarly b=2+2 nd c=3+3 nd d=4+4Now as abcd is cyclic quad. Then a+c=180° and b+d=180° now 1/2a+1/2c=90° similarly with b and d Now 1+3=90° and 3+4=90° And in ∆apd angle p=180°-(1+4)Similarly in ∆brc angle r=180°-(2+3)Add both equations nd replace the values of 1+3 nd 2+4 with 90°\'s and u will get p+r=180°Hence it is a cyclic quad.