Question

ABCD is a triangle in which AB equal to AC and D and e are the points on side the a b and ac respectively such that ad equal to e so that the point of BC and Dr cyclonic​

Answer 1

To prove -  B,C,D,E are concyclic .

Proof -  In Δ ADE

              AD  =  AE

       =>  ∠ADE  = ∠AED    (angles opposite to equal sides are    equal)

       Also,  ∠ADE + ∠BDE = ∠AED + ∠DEC     (Because linear pair is 180° )

       =>  ∠BDE = ∠DEC

       So , in quadrilateral BDEC

    ∠B + ∠C + ∠BDE + ∠DEC = 360°   (As, sum of angles in quadrilateral is of 360°)

      =>  2∠B  + 2∠DEC  =  360°

      =>  ∠B + ∠DEC  =  180°

Also, according to theorem, if opposite angles are supplementary , points are concyclic .

Thus, B,C,D,E are concyclic .