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Chords Ab and Cd of a Circle Intersect Each Other at Point P Such that Ap = Cp Show That: Ab = Cd - ICSE Class 10 - Mathematics

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ConceptArc and Chord Properties - If Two Chords Intersect Internally Or Externally Then the Product of the Lengths of the Segments Are Equal

Question

Chords AB and CD of a circle intersect each other at point P such that AP = CP

Show that: AB = CD

Solution


Given – two chords AB and CD intersect
Each other at P inside the circle
With centre O and AP = CP
To prove – AB = CD
Proof – Two chords AB and CD intersect each other inside the circle at P.
 ∴ AP × PB = CP× PD
⇒  `(AP )/(CP)= (PD) / (PB)`

But AP = CP    …….(1)          [given]

∴ PD = PB  or  PB = PD      ……. (2)
Adding (1) and (2)
AP + PB = CP + PD
⇒ AB = CD     

  Is there an error in this question or solution?
Solution Chords Ab and Cd of a Circle Intersect Each Other at Point P Such that Ap = Cp Show That: Ab = Cd Concept: Arc and Chord Properties - If Two Chords Intersect Internally Or Externally Then the Product of the Lengths of the Segments Are Equal.
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