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If x and y are the mid-points of the sides CA and CB respectively of a `∆ABC` right angled at C. prove that `4Ay^2=4AC^2 +BC^2`

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KALYANI PUBLICATION-PYTHAGORAS THEOREM-EXERCISE
  1. In an equilateral triangle with side 'a' prove that its altitudes = sq...

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  2. ABC is an isosceles triangle right angled at C.Prove thatAB^2=2AC^2.

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  3. If x and y are the mid-points of the sides CA and CB respectively of ...

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  4. If PB and AQ are the medians of a ∆ABC right angled at C. Prove that ...

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  5. If PB and AQ are the medians of a ∆ABC right angled at C. Prove that ...

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  6. If PB and AQ are the medians of a ∆ABC right angled at C. Prove that ...

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  7. ABC a right angle triangle, right angled at B. AD and CE are the media...

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  8. P and Q are points on the sides CA and CB of a ∆ABC , right angled at...

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  9. In ∆ABC , AD | BC such that AD^2 = BD.CD. Prove that ∆ABC is right ang...

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  10. ∆ABC is a right angled triangle right angled at A and AD | BC. Prove t...

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  11. ∆ABC is a right angled at B and D is mid-point of BC. Prove that AC^2 ...

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  12. ∆PQR is right angled at Q and the points S and T trisect the side QR. ...

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  13. In an equilateral triangle, prove that three times the square of one s...

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  14. In an equilateral triangle ABC, D is a point on side BC such that BD =...

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  15. ∆ABC is right angled at C and CD | AB. If BC = a , CA=b , AB = c and C...

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  16. Of triangle ABC,angleB=90^@ and BD|AC.IF AB=c,BC=a,CA=b and BD=p then ...

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  17. Two poles of heights 6 m and 11 m stand on a plane ground. If the dist...

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  18. Two poles of height 10 m and 15 m stand vertically on a plane ground. ...

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  19. In Fig.6.45,O is a point in the interior of a triangle ABC,OD|BC,OE|AC...

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  20. O is a point in the interior of ∆ABC. OD,OE and OF are the perpendicul...

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