Question

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

Show that: AB = CD

Answer 1

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