Question

in the figure, ABC is a triangle in which AB = AC . points D and E are points on the side AB and AC respectively such that AD= AE . show that the points B, C , E and D lie on a same circle

Answer 1

Step-by-step explanation:

FOREWORD. The two earliest of the nine main divisions of English Literature are by far the longest—taken

together are longer than all the others combined—but we shall pass rather rapidly over them.

Answer 2

Answer:

As, opposite angles are supplementary , so B , C , D and E are concyclic .

Step-by-step explanation:

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 .

Hence proved .