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Example 2 - If two intersecting chords of a circle make - Examples

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  1. Chapter 10 Class 9 Circles
  2. Serial order wise
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Example 2 If two intersecting chords of a circle make equal angles with the diameter passing through their point of intersection, prove that the chords are equal. Given: Let AB & CD be two chords intersecting at E. PQ is the diameter passing through E AB & CD makes equal angles with diameter PQ &., ∠ AEQ = ∠ DEQ To prove: Chords are equal i.e., AB = CD Construction: We draw OL ⊥ AB & OM ⊥ CD Proof: In ΔOLE and ΔOME, ∠OLE = ∠OME ∠OEL = ∠OEM OE = OE ∴ ΔOLE ≅ ΔOME OL = OM Here, OL is the distance of chord AB from centre & OM is the distance of chord CD from centre Since OL = OM, ∴ Chord AB & CD are equidistant from the centre So, AB = CD Hence proved

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