## shubhamsrg 2 years ago ABC is a triangle inscribed in a cirlce. AD and AE are straight lines drawn from A to the base BC parallel to the tangents at B and C respectively. given AB=5, AC=6 and CE=9 ,find length of BD

1. shubhamsrg

now there are 2 figures possible of this : |dw:1350459104532:dw| OR

2. shubhamsrg

|dw:1350459323053:dw|

3. sauravshakya

|dw:1350459526913:dw|

4. sauravshakya

I think that will lead to the solution.

5. sauravshakya

Triangle AEC , ADB and ABC are similar triangles.

6. shubhamsrg

how are they similar ?

7. shubhamsrg

and how did you get <A = @ ?

8. sauravshakya

Angle between a tangent and a chord at the point of contact is equal to the opposite inscribed angle.

9. sauravshakya

Also, AE=ED

10. sauravshakya

|dw:1350460037538:dw|

11. shubhamsrg

ohh,,so sorry !! from tge last 1/2 hr..i have been making the same mistake!!

12. shubhamsrg

yep..clear so far..

13. sauravshakya

So, Now can u?

14. shubhamsrg

allow me to try.

15. sauravshakya

OKAY!

16. shubhamsrg

cosine law right ?

17. sauravshakya

Nope.

18. sauravshakya

Similar triangles will do it.

19. shubhamsrg

why will they be similar? AEC and ADB ?

20. shubhamsrg

only 1 angle is common,,what else?

21. shubhamsrg

not common,,i mean equal*

22. sauravshakya

|dw:1350460670165:dw|

23. sauravshakya

First show triangle ABC and triangle AEC similar

24. shubhamsrg

i dont guess they are ? are they ?

25. sauravshakya

Triangle ABC and triangle AEC are similar....... u got this?

26. shubhamsrg

nops? which angle equals which in that similarity ?

27. shubhamsrg

ohh..got it,,got it..

28. shubhamsrg

ahh i see,,all 3 are similar then

29. sauravshakya

@shubhamsrg u got that?

30. shubhamsrg

yes i understand now..

31. shubhamsrg

and i got the ans.. its 25/4 .. thanks a ton1

32. sauravshakya

Welcome buddy