#### 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.