In `triangleABC, /_C= 90^(@)` and P and Q are the midpoints of BC and AC respectively. Prove that `AP^(2)+ BQ^(2)= 5PQ^(2)`.

In DeltaABC, /_B=90^(@) . D and E are any points on sides AB and BC respectively. Prove that AE^(2)+CD^(2)= AC^(2)+DE^(2) .

ABC is a right triangle right angled at B. Let D and E be any points on AB and BC respectively. Prove that AE^(2) + CD^(2) = AC^(2) + DE^(2) .

In triangleABC , P, Q and R are the midpoints of AB, BC and CA respectively . If ar(PBQR)=36 cm^2 , then ar(ABC)=____ cm^2

In triangleABC , P,Q and R are the midpoints of AB, BC and CA respectively. If ar(ABC)=32 cm^2 , then ar(PQR)= ____ cm^2

In DeltaABC , E and F are the midpoints of sides AB and AC respectively. If EF=5cm, find BC.

In triangleABC , P, Q and R are the midpoints of AB, BC and CA respectively . If ar(ABC)=____40 cm^2 , then ar(PBCR)= ____ cm^2

In Delta ABC , P, Q and R are the midpoints of AB, BC and CA respectively. If PQ = 5 cm, QR = 8 cm and RP = 6.5 cm, find the perimeter of Delta ABC .

In a right trianlge 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 9(AQ^(2)+BP^(2))= 13AB^(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 right angled DeltaABC, /_C= 90^(@) and D, E, F are three points on BC such that they divide BC in eaual parts (see the given figure). Prove that 8(AF^(2)+AD^(2))= 11AC^(2)+5AB^(2) .