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

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CALCUTTA BOOK HOUSE-PYTHAGORAS THEOREM -LONG-ANSWER TYPE QUESTION
  1. PQR is a triangle whose /Q is right angle. If S is any point on QR, t...

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  2. Prove that the sum of squares drawn on the sides of a rhombus is equal...

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  3. ABC is an equilateral triangle. AD is perpendicular to BC. Prove that ...

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  4. ABC is a right-angled triangle of which /A = right angle. P and Q are...

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  5. If the diagonals of the quadrilateral ABCD intersect each other orthog...

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  6. AD is the height of the triangle ABC. If AB gt AC,then prove that AB^...

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  7. Two perpendicular BD and CE are drawn from the vertices B and C respe...

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  8. ABC is a right-angled isoscels triangles of which /C is a right angle...

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  9. In Delta ABC,/A = right angle. If CD is a median, then prove that BC^(...

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  10. OX,OY and OZ are the perpendiculars drawn from an internal point O of ...

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

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

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

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

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

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

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

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

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

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

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