Question

prove that if two chords of a circle bisect each other their point of intersection will be the centre of the circle
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Answer 1

Let AB and CD be two chords intersecting at point O. Join AC and BD.

Now ΔAOC≈ΔBOD

⇒AC=BD

⇒∧AC =∧ BD-----------(1)

Now,

ΔAOD≈ΔBOC

⇒AD=BC

⇒∧AD=∧BC--------(2)

(1)+(2)

⇔∧AC+∧AD =∧BD+∧BC

⇒ ANGLE "CAD"= ANGLE "CBD"

Then CD divides the circle into two equal parts thus CD is a diameter

Similarly AB is also the diameter and they both meet at point O

Thus they bisect each other....

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Answer 2

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