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In an equilateral ` A B C` , `A D_|_B C` , prove that `A D^2=3\ B D^2`

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RD SHARMA-TRIANGLES-All Questions
  1. In a right A B C right-angled at C , if D is the mid-point of B...

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  2. In a quadrilateral A B C D , /B=90o , A D^2=A B^2+B C^2+C D^2 , pro...

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  3. In an equilateral A B C , A D|B C , prove that A D^2=3\ B D^2

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  4. A B D is a right triangle right-angled at A and A C|B D . Show t...

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

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  7. In each of the figures [4.222 (i)-(iv)] given below, a line segment...

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  8. In A B C , points P and Q are on C A and C B , respectively s...

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  9. In Fig. 4.224, D E C B . Determine A C and A E . (FIGURE)

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  10. In Fig. 4.225, given that A B C P Q R and quad A B C D q u a d\...

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  11. In A B C , P and Q are points on sides A B and A C respectively ...

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  12. In each of the following figures, you find two triangles. Indicate ...

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  13. In P Q R , M and N are points on sides P Q and P R respectively ...

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  14. In A B C , P and Q are points on sides A B and A C respectively ...

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  15. In Fig. 4.227, A M B C M D ; determine M D in terms of x ,\ y...

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  16. In A B C , the bisector of /A intersects B C in D . If A B=18 c m ...

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  17. In Fig. 4.228, l m (FIGURE) Name three pairs of similar triangl...

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  18. In Fig. 4.229, A B D C Prove that (FIGURE) D M U B M V (ii) ...

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  19. A B C D is a trapezium in which A B D C . P and Q are points on...

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

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