Two chords AB and CD of a circle intersect at a point P outside the circle. Prove that
(1) ΔPAC∼ΔPDB
(2) PA.PB=PC.PD.
(i) In ΔPAC and ΔPDB,
∠P=∠P(Common)
∠PAC=∠PDB (Exterior angle of a cyclic quadrilateral is ∠PCA=∠PBD equal to the opposite interior angle)
∴ΔPAC∼ΔPDB
(ii)We know that the corresponding sides of similar triangles are proportional.
∴PAPD=ACDB=PCPB
⇒PAPD=PCPB
∴PA.PB=PC.PD