In triangle ABC, AP, BQ and CR are the medians. Prove that `3[AB^(2)+BC^(2)+AC^(2)]=4[AP^(2)+BQ^(2)+CR^(2)]`.

ABCD is a rhombus. Prove that AC^(2) + BD^(2) = 4 AB^(2)

In an equilateral triangle ABC, AD _|_ BC . Prove that : AB^(2) + CD^(2) = 5/4 AC^(2)

In a right-angled DeltaABC right-angled at C, P and Q are the midpoints of BC and AC. Prove that AP^(2)+BQ^(2)=5PQ^(2) .

In Delta ABC , AD bot BC and AD^(2)= BD xx CD . Prove that AB^(2) + AC^(2) = (BD + CD)^(2)

In Fig . AD is a median of a triangle ABD and AM bot BC. Prove that : AC^(2)+AB^(2)=2AD^(2)+1/2 BC^(2)

In Delta ABC , DE || BC and CD || EF . Prove that AD^(2) = AF xx AB

In the given fig. if AD bot BC Prove that AB^(2) + CD^(2) = BD^(2) + AC^(2) .

In Delta ABC , BD : CD = 3 : 1 and AD _|_ BC . Prove that 2(AB^(2) - AC^(2)) = BC^(2) .

ABC is an isosceles triangle right angled at C . Prove that AB^(2)=2AC^(2) .

In Fig , ABC is a triangle in which angleABCgt90^(@) and AD bot CB, produced . Prove that AC^(2)=AB^(2)+BC^(2)+2BC.BD