P and Q are the mid-points of the sides CA and CB respectively of a `triangleABC` , right angled at C, prove that. (i) `4AQ^(2)=4AC^(2)+BC^(2)` (ii) `4BP^(2)=4BC^(2)+AC^(2)`

P and Q are the mid-points of the sides CA and CB respectively of a Delta ABC , right angled at C. Prove that 4(AQ^(2)+BP^(2))=5 AB^(2) .

If x and y are the mid-points of the sides CA and CB respectively of a ∆ABC right angled at C. prove that 4Ay^2=4AC^2 +BC^2

P and Q are the mid point of the sides CA and CB respectively of a triangle ABC, right angled at C. then, find the value of 4 (AQ^(2) + BP^(2) ) .

P and Q are the mid-points of the CA and CD respectively of a triangle ABC, right angled at C. Prove that: 4AQ^2 = 4AC^2 + BC^2 , 4BP^2 = 4BC^2 + AC^2 , and 4(AQ^2 + BP^2) = 5AB^2 .

P and Q are points on the sides CA and CB respectively of ABC, right angled at C. Prove that AQ^(2)+BP^(2)=AB^(2)+PQ^(2)

In a right triangle ABC right angled at C, P and Q are points on sides AC and CB respectively which divide these sides in the ratio of 2 : 1. Prove that (i) 9 AQ^(2) = 9AC^(2) + 4BC^(2) (ii) 9BP^(2) = 9BC^(2) + 4AC^(2) (iii) 9 (AQ^(2) + BP^(2)) = 13 AB^(2)

In a right triangle ABC right angled at C, P and Q are points on sides AC and CB respectively which divide these sides in the ratio of 2 : 1. Prove that (i) 9 AQ^(2) = 9AC^(2) + 4BC^(2) (ii) 9BP^(2) = 9BC^(2) + 4AC^(2) (iii) 9 (AQ^(2) + BP^(2)) = 13 AB^(2)

P and Q are points on the sides CA and CB of a ∆ABC , right angled at C. Prove that AQ^2 + BP^2 = AB^2 + PQ^2 .

D,E and F are mid-points of the sides BC, CA and AB respectively of triangleABC . Prove that ar(triangleDEF) = 1/4 ar (triangleABC)