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Theorems on Chord and Subtended AngleHere we will discuss some theorems on chord and subtended angle.In this Circle Theorems, the theorems are based on equal chord. Here, we shall also study theorems on subtended angles and the relationship between the lengths of chords and their distances from the center of the given circle. Theorems on Chord and Subtended Angle 1) Equal chords of a circle are equidistant from the center. Given : Two chords AB and CD of circle C(O,r) such that AB = CD and OL ⊥ CD. Prove that : Chords AB and CD are equidistant from the center i.e. OM = OL Construction : Join OA and OC.
Given : AB = CD Prove that : ∠AOB = ∠COD
3) Angles in the same segment of a circle are equal. Given: A circle C(O,r), an arc PQ and two angles ∠PRQ and ∠PSQ in the same segment of the circle. Prove: ∠PRQ = ∠PSQ Construction: Join OP and OQ.
Theorems on Circle • Theorems on Chord • Theorems on Chord and Subtended Angle • Theorems on Arc and Angle • Theorems on Cyclic Quadrilateral
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