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)` .

If ABC is a right triangle right-angled at B and M, N are the midpoints of AB and BC respectively. Then 4 (AN^2 + CM^2) =

In the given figure, ABC is a triangle right angled at B. D and E are ponts on BC trisect it. Prove that 8AE^(2) = 3AC^(2) + 5AD^(2) .

In a right triangle ABC right-angled at B, if P and Q are points on the side AB and AC respectively, then___

In Delta ABC, AD_|_ BC . Prove that AB^(2) - BD^(2) =AC^(2) -CD^(2)

ABC is a right-angled triangle of which /_A = right angle. P and Q are two points on AB and AC respectively.By joining P,Q,B,Q and C,P prove that BQ^(2) + PC^(2) = BC^(2) + PQ^(2)

ABC is a right-angled isoscels triangles of which /_C is a right angle. If D is any point on AB. Then prove that AD^(2) + BD^(2) = 2CD^(2)

In the right-angled ABC, /_A =1 right angle. BE and CF are two medians of Delta ABC . Prove that 4 ( BE^(2) + CF^(2)) =5 BC^(2)

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

ABC is a right angled triangle right angled at B. If P and Q are the mid - points of the sides overline(AB)andoverline(BC) respectively , then show that , 4(AQ^(2)+PC^(2))=5AC^(2) .