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Fig.6.45,O is a point in the interior of...

Fig.6.45,O is a point in the interior of a triangle ABC,`OD_|_BC,OE_|_AC and OF_|_AB`.Show that
(ii)`AF^2+BD^2+CE^2=AE^2+CD^2+BF^2`

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In Fig.6.45,O is a point in the interior of a triangle ABC, OD_|_BC,OE_|_AC and OF_|_AB .Show that (i) OA^2+OB^2+OC^2-OD^2-OE^2-OF^2=AF^2+BD^2+CE^2

D is a point on the side BC of a triangle ABC such that angleADC=angleBAC .Show that CA^2=CB.CD .

In Fig.6.60, AD is a median of a triangle ABC and AM_|_BC .Prove that :(iii) AC^2+AB^2=2AD^2+1/2BC^2

In Fig.6.60, AD is a median of a triangle ABC and AM_|_BC .Prove that :(ii) AB^2=AD^2-BC.DM+((BC)/2)^2

If A,B and C are interior angle of a triangle ABC,then show that sin(B+C)/2=cos(A/2)

In Fig.6.60, AD is a median of a triangle ABC and AM_|_BC .Prove that :(i) AC^2=AD^2+BC.DM+((BC)/2)^2

In the right triangleACB, angleC=90^@ and CD_|_AB .Prove that, (BC^2)/(AC^2)=(BD)/(AD)

D and E are points on the sides CA and CB respectively of a triangle ABC right angled at C.Prove that, AE^2+BD^2=AB^2+DE^2 .

O is a point in the interior of ∆ABC . OD,OE and OF are the perpendicular drawn to the sides BC, CA and AB respectively. Prove that AF^2+BD^2+CE^2=AE^2+BF^2+CD^2 .

In Fig.6.53,ABD is a triangle right angle at A and AC_|_BD .Show that (ii) AC^2=BC.DC .

R G PUBLICATION-TRIANGLES-EXERCISE
  1. Prove that the sum of the squares of the sides of a rhombus is equal t...

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

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

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  4. A ladder 10 m long reaches a window 8m above the ground. Find the dist...

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  5. A guy wire attached to a vertical pole of heigh 18 m is 24 m long and ...

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  6. An aeroplane leaves an airport and flies due north at a speed of 1000 ...

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

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  8. D and E are points on the sides CA and CB respectively of a triangle A...

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  9. The perpendicular from A on side BC of atriangleABC intersects BC at ...

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

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

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  12. Tick the correct answer and a justify :In triangleABC,AB=6sqrt3,AC=12c...

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  13. In Fig.6.56,PS is the bisector of angleQPR of trianglePQR.Prove that (...

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  14. In Fig.6.57, D is point on hypothenuse AC of triangleABC,such thatBD|A...

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  15. In Fig.6.58, ABC is a triangle in which angleABC>90^@ and AD|CBproduce...

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  16. In Fig.6.59, ABC is a triangle in which angleABC<90^@ and AD|BC.Prove ...

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  17. In Fig.6.60, AD is a median of a triangle ABC and AM|BC.Prove that :(i...

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  18. In Fig.6.60, AD is a median of a triangle ABC and AM|BC.Prove that :(i...

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  19. In Fig.6.60, AD is a median of a triangle ABC and AM|BC.Prove that ...

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  20. In Fig.6.61, two chords AB and CD intersect each other at the point P....

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