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A point `D` is on the side `B C` of an equilateral triangle `A B C` such that `D C=1/4\ B C` . Prove that `A D^2=13\ C D^2` .

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RD SHARMA-TRIANGLES-All Questions
  1. 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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  2. 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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  3. A point D is on the side B C of an equilateral triangle A B C su...

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

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  6. 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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  7. 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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  8. 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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  9. Prove that in an equilateral triangle, three times the square of a ...

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  10. 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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  11. In a quadrilateral A B C D ,\ \ /B=90o . If A D^2=A B^2+B C^2+C D^2...

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  12. In a triangle A B C , N is a point on A C such that B N|A C . If...

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  13. Nazinia is fly fishing in a stream. The tip of her fishing rod is 1...

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  14. State basic proportionality theorem and its converse.

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  15. In the adjoining figure, find A C . (FIGURE)

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  16. In the adjoining figure, if A D is the bisector of /A , what is ...

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  17. State AAA similarity criterion.

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  18. State S S S similarity criterion.

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  19. State S A S similarity criterion.

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  20. In the adjoining figure, D E is parallel to B C and A D=1c m, B D=2c m...

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