In the Fig. AD and BE are medians of `DeltaABC and BE"||"DF`. Prove that `CF=(1)(4)AC.`

In Fig . AD is a median of a triangle ABD and AM bot BC. Prove that : AC^(2)=AD^(2)+BC. DM+((BC)/(2))^(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 Fig . AD is a median of a triangle ABD and AM bot BC. Prove that : AB^(2)=AD^(2)-BC.DM+((BC)/(2))^(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 an isosceles DeltaABC,AB=ACandBD_|_AC . Prove that BD^(2)-CD^(2)=2CD.AD .

In Fig DE||AC and AE . Prove that (BF)/(FE) = (BE)/(EC)

BL and CM are medians of a triangle ABC right angled at A. Prove that 4(BL^(2) + CM)^(2) = 5 BC^(2) .

In the figure 11.23, E is any point on median AD of a Delta ABC. Show that ar (ABE) = ar (ACE).

In Fig . D is a point on hypotenuse AC of DeltaABC, bot DM botBCand DNbot AB. prove that : DM^(2)=DN.MC