Question

plz solve this question quickly.

Answer 1

Given that AB and CD are two chords of a circle, with centre O intersecting at a point E.
XY is a diameter passing through E, such that ∠ AEY = ∠ DEY
Draw OP⊥ AB and OQ ⊥ CD.
In right angled DOPE
∠POE + 90° + ∠ PEO =180° (Angle sum property of a triangle)
 ∴∠POE = 90° – ∠PEO  
= 90° – ∠AEY = 90° – ∠DEY
= 90° – ∠QEO = ∠QOE
In triangles OPE and OQE,
∠PEO = ∠QEO        
∠POE = ∠QOE (Proved)
OE = OE (Common side)
∴ ΔOPE ≅ ΔOQE       
⇒ OP = OQ (CPCT)
Thus, AB = CD