1. anonymous

2. anonymous

@Michele_Laino help me once again

3. anonymous

British curriculum?

4. anonymous

what ?

5. Michele_Laino

6. anonymous

okay...

7. Michele_Laino

here is my reasoning: |dw:1434709278703:dw| we have: $\Large L = 2r\sin x$

8. anonymous

thank you...

9. Michele_Laino

now, using the theorem of Pitagora, we can write: $\begin{gathered} \sqrt {4{r^2} - A{B^2}} = 2r\sin x \hfill \\ \sqrt {4{r^2} - A{B^2}} = 2r\sqrt {1 - {{\left( {\cos x} \right)}^2}} \hfill \\ 2r\sqrt {1 - {{\left( {\frac{{AB}}{{2r}}} \right)}^2}} = 2r\sqrt {1 - {{\left( {\cos x} \right)}^2}} \hfill \\ \end{gathered}$

10. Michele_Laino

$\Large \begin{gathered} \sqrt {4{r^2} - A{B^2}} = 2r\sin x \hfill \\ \sqrt {4{r^2} - A{B^2}} = 2r\sqrt {1 - {{\left( {\cos x} \right)}^2}} \hfill \\ 2r\sqrt {1 - {{\left( {\frac{{AB}}{{2r}}} \right)}^2}} = 2r\sqrt {1 - {{\left( {\cos x} \right)}^2}} \hfill \\ \end{gathered}$

11. Michele_Laino

so, by comparison, we can write: $\large \cos x = \frac{{AB}}{{2r}}$

12. Michele_Laino

now, using the condition of your problem, we can write: $\large \begin{gathered} AB + AC + arc(BC) = \pi r \hfill \\ 2AB + 2xAB = \pi r \hfill \\ 2AB\left( {1 + x} \right) = \pi r \hfill \\ AB = \frac{{\pi r}}{{2\left( {1 + x} \right)}} \hfill \\ \end{gathered}$ since, by definition of radians we can write: $\large arc(BC) = 2xAB$

13. Michele_Laino

now substitute the value of AB, into the expression for cos x, what do you get?

14. alekos

brilliant!

15. Michele_Laino

thanks!! :) @alekos

16. anonymous

thanks @Michele_Laino

17. Michele_Laino

:) @yajna

18. alekos

it all follows through quite nicely. how the hell you came up with that so quickly astounds me

19. anonymous

@Michele_Laino is a genius @alekos

20. anonymous

btw @yajna this is the hardest question of this type you can hope to find in p3. So don't stress yourself too much if you find it hard the first time.

21. Miracrown

A true genius she is! @Michele_Laino :)

22. anonymous

yes...

23. Michele_Laino

thanks! @Miracrown

24. alekos

@michele what do you do for a living?

25. Michele_Laino

at the moment I have no job!

26. alekos

you've got to be kidding! what sort of job are you looking for?

27. Michele_Laino

for example teacher, draftsman or translator from English to Italian. my last job was to translate texts of patents

28. Michele_Laino

from English to Italian

29. Michele_Laino

and my preceding job was nautical draughtsman

30. alekos

have you been out of work for long?

31. Michele_Laino

at the moment I am without job from at least 10 months!

32. alekos

i am sure you will find another job soon. keep looking and it will happen. you're a smart lady and you deserve it.

33. Michele_Laino

Thanks for your encouragement!! :) nevertheless, please keep in mind that I'm a male, Lol!!