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.

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
view all courses