Question

In the adjoining figure, P is the centre of the circle. Chord AB and chord CD intersect on the diameter at

the point E. If ∠AEP ≅ ∠DEP, then prove that AB = CD. What is the bisector of seg ES​

Answer 1

Answer:

Construction : Draw perpendicular from point to the chord CD and AB 

To prove : AB=CD 

Proof : In △MEP and △NEP

∠EMP=∠ENP=90∘

∠AEP=∠DEP(Given) 

EP=EP(common)

Thus, by AAS congruence rule, △MEP≅△NEP 

So, MP=NP(CPCT)  

We know that chords equidistant from the centre are equal to each other. 

Hence , AB=CD