Question

4. In the figure, ABC is a triangle in which AB = AC . Points Dand 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

Answer:

Step-by-step explanation:

Given :-

AB = AC

AD = AC

To Prove :-

Points B, C, E and D lie on a same circle.​

Solution :-

Since, AB = AC .....(i) and AD = AC...... (ii)

Subtracting AD from both sides, we get:  

⟹ AB - AD = AC - AD  

⟹ BD = EC …(iii)  (Since, AD = AE)  

Dividing equation (ii) by equation (iii), we get:

AD/DB = AE/EC

Applying the converse of Thales’ theorem, DE‖BC  

⟹ ∠DEC + ∠ECB = 180°

⟹ ∠DEC + ∠CBD = 1800 (Since, AB = AC ⇒ ∠B = ∠C)  

Therefore, quadrilateral BCED is cyclic.

Hence, B,C,E and D are concylic points.

Answer 2

hope this helps you

please mark the answer as brainliest

please FOLLOW me