Q. 123.8( 18 Votes )

In the adjoining

Answer :

Given: AD = AE …(i)

& AB = AC …(ii)


Subtracting AD from both sides of equation (ii), we get


AB – AD = AC – AD


AB – AD = AC – AE [from equation (i)]


DB = EC [ AB – AD = DB & AC – AE = EC] …(iii)


Now, divide equation (i) by (iii), we get



By converse of Thale’s theorem, we can conclude by this equation that DE BC.


So, DEC + ECB = 180° [ sum of interior angles on the same transversal line is 180°]


Or DEC + DBC = 180° [ AB = AC C = B]


Hence, we can write DEBC is cyclic and points D, E, B and C are concyclic.


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