Asked by hemant2020 | 4th Feb, 2010, 09:13: PM
let ABCD be the quadrilateral.
let the angle bisectors of angles A and B meet at P
that of C and D meet at Q.
so a quadrilateral is formed with P and R as two of its vertices.
let the other two vertices be Q and S, so that the quadrilateral is PQRS.
consider triangle DQC,
angle Q+(C/2)+(D/2)=180....(i) angle sum property.
in triangle APB.
ading (i) and (ii) and using the fact that sum of the angles A,B,C,D is 360 degrees
angle P+ angle Q=180
so quadrilateral PQRS is cyclic as opp angles are supplementary.
Answered by | 4th Feb, 2010, 11:23: PM
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