Class 9 Maths Circles Angle subtended by a chord at a point

Angle subtended by a chord at a point

Cord AB subtends 3 angles

  1. Angle 1 on Major arc
  2. Angle 2 on Minor arc
  3. Angle 3 on Center of circle

 

 

Let’s try to figure our relation between length of chord & angle subtended and the center.

In the given figure chord DE= FG = HI. It is observed that ∠ A = ∠ B =∠ C ,

Thus we conclude that Equal chords of a circle subtend equal angles at the centre.

 

Theorem 1: Equal chords of a circle subtend equal angles at the centre

Refer ExamFear video lessons for Proof of this theorem.

 

The converse is also true.

Converse Theorem 2: If the angles subtended by the chords of a circle at the centre are equal, then the chords are equal.

Refer ExamFear video lessons for Proof of this theorem.

 

 

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