N isosceles triangle ABC with AB=AC,a circle passing through b and c INTERSECTSTHE SIDES AB AND intersects the sides ABand AC AT D and E respectively .prove thatDE is parallel to side BC

N isosceles triangle ABC with AB=AC,a circle passing through b and c

1.	N isosceles triangle ABC with AB=AC,a circle passing through b and c INTERSECTSTHE SIDES AB AND intersects the sides ABand AC AT D and E respectively .prove thatDE is parallel to side BC
Answer» e that DE is parallel to BC,if we prove that angle ADE = Angle ABC , hence it will be proved because of corresponding angle propertyso we will prove it firstIn ΔABC,∠B = ∠C .... (1)In the CYCLIC quadrilateral CBDE, side BD is produced to A.We know that exterior angle is equal to opposite interior angle.i.e. ∠ADE = ∠C .... (2)From (1) and (2) –∠ADE = ∠ABCSO corresponding angles are equalAns. hence DE is parrallel to BCNote:-Required Diagram is in attachment!