Question

Prove that if two chords of a circle bisect each other , then the two chords are diameters of the given circle.


plzzzzzzz fast!!!!

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....
Refer the attachment for the diagram

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Answer 2

Answer:

Step-by-step explanation is given in the picture.... Thanks!!