Q12 of 62 Page 180

In a quadrilateral ABCD, the bisectors of ∠B and ∠D intersect on AC at E.

Prove that .

Given: quadrilateral ABCD with bisectors at B and D intersecting at e on AC


Required: To Prove


Consider ΔABC, here BE is the angle bisector of ∠B


∴ By Angle bisector theorem we have, --eq(1)


Now, Consider ΔADC, here DE is the angle bisector of ∠D


∴ By Angle bisector theorem we have, --eq(2)


From –eq(1) and –eq(2)


We have,



Hence proved


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