Example 2: Iftwo intersectpassing through their point of intersection, prove that the chords are equal.ing chords of a circle make equal angles with the diameter

Example 2: Iftwo intersectpassing through their point of intersection,

1.	Example 2: Iftwo intersectpassing through their point of intersection, prove that the chords are equal.ing chords of a circle make equal angles with the diameter
Answer» 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 = ∠ DEYDraw 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 = ∠QOEIn triangles OPE and OQE,∠PEO = ∠QEO ∠POE = ∠QOE(Proved)OE = OE (Common side)∴ ΔOPE ≅ ΔOQE ⇒ OP = OQ (CPCT)Thus,AB = CD