. Prove that the angle bisectors of the angle formed by producing opposite sides of a cyclic quadrilateral (provided they are not parallel) intersect at
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Sol: Given : ABCD is a cyclic quadrilateral in which its opposite sides AD and BC are produced to meet at P and opposite sides AB and DC produced to meet at Q. PM is the bisector of ÐAPB and QM is the bisector of ÐAQD. They meet at the point M.
To prove: ÐPMQ = 90°
Construction: Produce PM to meet AB in N.
Proof: In triangles PDL and PBN, we have
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