$P$ is a point on the common chord $R S$ produced by two intersecting circles. $A B$ and $C D$ are the chords of the circles,they meet at $P$ produced.Prove that $P A \times P B = P C \times P D$

Open in App

Solution

Two chords $A B$ and $R S$ of the first circle meet externally at $P$
$P A \times P B = P R \times P S$ ....... $(1)$
Two chords $C D$ and $R S$ of the second circle meet externally at $P$
$P C \times P D = P R \times P S$ ....... $(2)$
From $(1)$ and $(2)$
$P A \times P B = P C \times P D$

Suggest Corrections

Similar questions

AB & CD are two equal chord of circle with centre o. If AB and CD, on being produced, meet at a point P outside the circle, Prove that: (i) PA = PC (ii) PB = PD

Q. In given Fiig., two chords AB and CD of a circle intersect each other at the point P (when produced) outside the circle. Prove that

(i)

Δ PAC~ Δ PDB

(ii) PA . PB = PC . PD

A B

and

C D

are two chords of a circle intersecting at

P

. Prove that

A P \times P B = C P \times P D

Q. In Fig., two chords AB and CD of a circle intersect each other at the point P (when produced) outside the circle. Prove that:
(i)

△ P A C \sim △ P D B

(ii)

P A . P B = P C . P D

Q. Two chords AB and CD intersect at point P inside the circle. Find PD if PA = 6 cm, PB = 3 cm and PC = 2 cm.

Join BYJU'S Learning Program

P is a point on the common chord RS produced by two intersecting circles.AB and CD are the chords of the circles,they meet at P produced.Prove that PA×PB=PC×PD

Two chords AB and RS of the first circle meet externally at PPA×PB=PR×PS .......(1)Two chords CD and RS of the second circle meet externally at PPC×PD=PR×PS .......(2)From (1) and (2)PA×PB=PC×PD

$P$ is a point on the common chord $R S$ produced by two intersecting circles. $A B$ and $C D$ are the chords of the circles,they meet at $P$ produced.Prove that $P A \times P B = P C \times P D$

Two chords $A B$ and $R S$ of the first circle meet externally at $P$
$P A \times P B = P R \times P S$ ....... $(1)$
Two chords $C D$ and $R S$ of the second circle meet externally at $P$
$P C \times P D = P R \times P S$ ....... $(2)$
From $(1)$ and $(2)$
$P A \times P B = P C \times P D$