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

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.

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, ∠1 = ∠2 and ∠3 = ∠4. Show that PT × QR = PR × ST.