Login

prove that if two chords of a cicle bisect each other , then the two chords are diameter of the given circle.

Let AB and CD be 2 chords intersecting at point O. Join AC and BD.

Now, ΔAOC ΔBOD.

⇒AC = BD

Again, ΔAOD ΔBOC.

⇒AD = BC

On adding equations (1) and (2), we get

Them CD divides the circle into 2 semi-circles.

Hence, CD is a diameter.

Similarly, AB is a diameter.

  • 29
View Full Answer
  • name the diameter AC and the other BD
  • let the point of intersection be O
  • Join A,B,C,D
  • It will make parallelogram because AC bisects BD at O
  • in a parallelogram oppsites are equal (theorem)
  • therefore,
  • in a cyclic quadrilateral sum of opposite angles are supplementry (theorem), it means sum of opposite angles are 180 degree
  • therefore,
  • 2
  • in a circle diameter is the only chord which subtends 90 degree at the remaining part.
  • we had proved that AC is the diameter
  • centre is the only point where the diameter can bisect . so we had also proved that O is the centre.
  • any line that pass through the centre is the diameter.
  • therefore, BD is also diameter which passes through the centre O.
  • 15
What are you looking for?