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ABC is a isosceles right angled triangle, right angled at C. prove that ` AB^(2) = 2AC^(2)`

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Let the complex numbers Z_(1), Z_(2) and Z_(3) are the vertices A, B and C respectively of an isosceles right - angled triangle ABC with right angle at C, then the value of ((Z_(1)-Z_(2))^(2))/((Z_(1)-Z_(3))(Z_(3)-Z_(2))) is equal to

Delta ABD is a right triangle, right-angled at A and AC _|_ BD . Prove that AB^2 = BCxxBD .

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P and Q are the mid-points of the CA and CD respectively of a triangle ABC, right angled at C. Prove that: 4AQ^2 = 4AC^2 + BC^2 , 4BP^2 = 4BC^2 + AC^2 , and 4(AQ^2 + BP^2) = 5AB^2 .

NAGEEN PRAKASHAN ENGLISH-TRIANGLES -Exercise 6d
  1. The side of a rhombus is 13 cm. if one if the diagonals is 24 cm, find...

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  2. In the adjoining figure: anglePSQ= 90^(@) , PQ= 10 cm , QS = 6cm and R...

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  3. ABC is a isosceles right angled triangle, right angled at C. prove tha...

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  4. triangleABC is an isosceles triangle with AC = BC. If AB^(2)= 2AC^(2) ...

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  5. In an equilateral triangleABC, AD is the altitude drawn from A on the ...

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  6. M and N are point on sides QR and PQ respectively of /\ PQR, right-an...

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  7. The given figure shows a triangle ABC, in which AB gt AC. E is the mi...

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  8. In a square ABCD, show that AC^(2) = 2AB^(2).

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  9. In a rhombus ABCD, prove that AC^(2) + BD^(2) = 4AB^(2)

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  10. In triangle ABC, angle A =90^(@), CA=AB and D is a point on AB produce...

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  11. In acute angled triangle ABC, AD is median and AE is altitude , prove...

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  12. The following figure shows a triangle ABC in which AD is a median and ...

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  13. From a point O in the interior of a A B C , perpendiculars O...

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  14. In an acute angled triangle ABC, AD is the median in it. then : AD^...

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  15. In a right triangle ABC, right angled at A, AD is drawn perpendicular ...

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  16. In the given figure , ABC is a right triangle, right angled at B. Medi...

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  17. In the given figure , angleQPR= 90^(@) QR = 26 cm PM = 6cm, MR = 8c...

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  18. Given a right angled triangleABC. The lengths of the sides containing ...

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  19. In an acute-angled triangle, express a median in terms of its sides...

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  20. In a quadrilateral ABCD, angleB=90^(@) and AD^(2)= AB^(2) + BC^(2)+CD^...

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