In a right triangle ABC right-angled at C, P and Q are the points on the sides CA and CB respectively, which divide these sides in the ratio 2:1.Prove that [4 MARKS](i) 9AQ2=9AC2+4BC2(ii) 9BP2=9BC2+4AC2(iii) 9(AQ2+BP2)=13AB2

In a right triangle ABC right-angled at C, P and Q are the points on t

1.	In a right triangle ABC right-angled at C, P and Q are the points on the sides CA and CB respectively, which divide these sides in the ratio 2:1.Prove that [4 MARKS](i) 9AQ2=9AC2+4BC2(ii) 9BP2=9BC2+4AC2(iii) 9(AQ2+BP2)=13AB2
Answer» In a right triangle ABC right-angled at C, P and Q are the points on the sides CA and CB respectively, which divide these sides in the ratio 2:1. Prove that [4 MARKS] (i) $9 A Q^{2} = 9 {A C}^{2} + 4 {B C}^{2}$ (ii) $9 {B P}^{2} = 9 {B C}^{2} + 4 {A C}^{2}$ (iii) $9 ({A Q}^{2} + {B P}^{2}) = 13 {A B}^{2}$