In the figure (2) given below, medians BE and CF of a △ABC meet at G. Prove that :

(i) △FGE ~ △CGB

(ii) BG = 2GE

In the adjoining figure, AB = AC. If PM ⊥ AB and PN ⊥ AP, show that PM × PC = PN × PB.

In the figure (1) given below, ∠AED = ∠ABC. Find the values of x and y.

In the given figure, P is a point on AB such that PB : AP = 3 : 4 and PQ || AC.

(i) Calculate PQ : AC.

(ii) If AR ⊥ CP, QS ⊥ CB and QS = 6 cm, calculate the length of AR.