Question

if two intersecting chords of a circle make equal angles with the diameter passing through the point of intersection prove that the chords are equal with a diagram

Answer 1

Answer:

Step-by-step explanation:

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  

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hope this answer helps you  

Answer 2

Answer:

Here is the answer.......

Hope you understand it