Mathematics
In the figure (ii) given below, chords BA and DC of a circle meet at P. Prove that
(i) ∠PAD = ∠PCB
(ii) PA × PB = PC × PD.

Related Questions
In adjoining figure, AB = 9 cm, PA = 7.5 cm and PC = 5 cm. Chords AD and BC intersect at P.

(i) Prove that Δ PAB ∼ Δ PCD.
(ii) Find the length of CD.
(iii) Find the area of Δ PAB : area of Δ PCD.
In the figure (i) given below, QPX is the bisector of ∠YXZ of the triangle XYZ. Prove that XY : XQ = XP : XZ.

If O is the center of the circle find the value of x in the following figure (using the given information) :

If O is the center of the circle find the value of x in the following figure (using the given information) :
