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If in DeltaABC, AD| BC,then prove that A...

If in `DeltaABC, AD_|_ BC,`then prove that `AB^(2) + CD^(2) = AC^(2) + BD^(2)`

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

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

If the diagonals of the quadrilateral ABCD intersect each other orthogonally,then prove that AB^(2) + CD^(2) = BC^(2) + DA^(2)

In Delta ABC , AD is a median and AM _|_ BC.Prove that (a) AC^(2) = AD^(2) +BC.DM+ ((BC)/(2))^(2) (b) AB^(2) = AD^(2) -BC.DM+ ((BC)/(2))^(2) (c ) AC^(2) + AB^(2) = 2AD^(2) +(1)/(2) BC^(2)

In Delta ABC,/_A = right angle. If CD is a median, then prove that BC^(2) = CD^(2)+ 3AD^(2) .

In Delta ABC , AD_|_ BC which intersects BC at D. If BD =3 CD , then prove that 2AB^(2) = 2AC^(2)+BC^(2)

Delta ABC is an obtus triangle in which /_B = obtus angle. If AD is perpendicular to BC ( or extended BC ) ,then prove that AC^(2) = AB^(2) +BC^(2) + 2BC xx BD .

ABC is an equilateral triangle. AD is perpendicular to BC. Prove that AB^(2) + BC^(2) + CA^(2) =4AD^(2)

CD and GH are the bisectors of /_ACB and /_EGF respectively. If D lies on AB of DeltaABC and H lies on EF of DeltaEFG and if DeltaABC~DeltaEFG , then prove that (a) (CD)/(GH)=(AC)/(FG) , (b) DeltaDCB~DeltaHGE , (c ) DeltaDCA~DeltaHGF

CALCUTTA BOOK HOUSE-PYTHAGORAS THEOREM -LONG-ANSWER TYPE QUESTION
  1. OX,OY and OZ are the perpendiculars drawn from an internal point O of ...

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  2. In the Delta RST, /S right angle.X and Y are the midpoints of RS and ...

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  3. If in DeltaABC, AD| BC,then prove that AB^(2) + CD^(2) = AC^(2) + BD^...

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  4. Prove that the area of the square drawn on the diagonal of a square is...

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  5. O is any point inside a rectangle ABCD, Prove that OA^(2) + OC^(2)= OB...

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  6. ABCD is a rhombus.Prove that AB^(2) + BC^(2) +CD^(2) + DA^(2) = AC^(2)...

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  7. In Delta ABC, AD| BC . Prove thatAB^(2) - BD^(2) =AC^(2) -CD^(2)

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  8. In Delta ABC , AD| BC which intersects BC at D. If BD =3 CD, then pro...

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  9. In the isosceles triangle ABC, AB=AC and BE is perpendicular to AC fro...

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  10. In an isosceles right-angled triangle ABC,/B=90^(@). The bisector of /...

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  11. Prove that the sum of the areas of the squares drawn on the sides of a...

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  12. Delta PQR is a right-angled isosceles triangle of which the two sides...

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  13. P is an external point of the square ABCD. If PA gt PB ,then prove tha...

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  14. In the right-angled ABC, /A =1 right angle. BE and CF are two medians...

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  15. A perpendicular AD is drawn on BC from the vertex A of the acute Delta...

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  16. Prove that if equilateral triangles are drawn on the sides of a right-...

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  17. O is an internal point of the rectangle PQRS. Prove that OQ^(2)+OS^(2)...

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  18. In the right-angled triangle ABC,/C = 90^(@).If the length of perpendi...

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  19. Delta ABC is an equilateral triangle . D is a point on the side BC su...

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  20. Prove that if the difference of the areas of the squares drawn on any...

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