9.1-Angle Subtended by a Chord at a Point

9.1-Angle Subtended by a Chord at a Point Important Formulae

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Grade 9 → Math → Circles → 9.1-Angle Subtended by a Chord at a Point

After successful completion of this topic, you should be able to:

  • Understand angle subtended by a chord at a point.

Theorem 9.1 : Equal chords of a circle subtend equal angles at the centre.:

Theorem 9.2 : If the angles subtended by the chords of a circle at the centre are equal, then the chords are equal.:


Luca Antonelli (Luke Antony), CC BY-SA 3.0, via Wikimedia Commons

Recall that two circles are congruent if they have the same radii. Prove that equal chords of congruent circles subtend equal angles at their centres.

Solution:
Prove exactly as Theorem 9.1 by considering chords of congruent circles.

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Prove that if chords of congruent circles subtend equal angles at their centres, then the chords are equal.

Solution:
Use SAS axiom of congruence to show the congruence of the two triangles.

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