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