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`A B C D` is a trapezium having `A B D C` . Prove that `O` , the point of intersection of diagonals, divides the two diagonals in the same ratio. Also prove that `(a r( O C D))/(a r( O A B))=1/9` , if `A B=3\ C D` .

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RD SHARMA-TRIANGLES-All Questions
  1. A B C D is a trapezium in which A B D C . P and Q are points on...

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  2. In A B C ,\ D and E are points on sides A B and A C respectively ...

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  3. A B C D is a trapezium having A B D C . Prove that O , the poin...

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  4. Corresponding sides of two triangles are in the ratio 2\ :3 . If th...

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  5. The areas of two similar triangles are 36\ c m^2 and 100\ c m^2 . I...

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  6. Corresponding sides of two similar triangles are in the ratio 1:3 ....

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  7. In Fig. 4.230, each of P A ,\ Q B ,\ R C and S D is perpendicula...

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  8. In A B C , ray A D bisects /A and intersects B C in D . If B C=a , ...

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  9. In each of the figures given below, an altitude is drawn to the hyp...

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  10. There is a staircase as shown in Fig. 4.232, connecting points A an...

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  11. In A B C ,\ \ /A=60o . Prove that B C^2=A B^2+A C^2-A B.A C .

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  12. In A B C , /C is an obtuse angle. A D|B C and A B^2=A C^2+3\ B C^2...

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  13. A point D is on the side B C of an equilateral triangle A B C su...

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  14. In A B C , if B D|A C and B C^2=2\ A C C D , then prove that A B=...

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  15. In a quadrilateral A B C D , given that /A+/D=90o . Prove tha...

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  16. In A B C , given that A B=A C and B D|A C . Prove that B C^2=2\...

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  17. A B C D is a rectangle. Points M and N are on B D such that A M|B D...

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  18. In A B C , A D is a median. Prove that A B^2+A C^2=2\ A D^2+2\ D C...

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  19. Prove that in an equilateral triangle, three times the square of a ...

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  20. In a A B C , /A B C=135o . Prove that A C^2=A B^2+B C^2+4\ a r( A ...

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