Question

please helpppppppp...... medals and fan
question in comments

Answer 1

@Michele_Laino help me once again

Answer 2

British curriculum?

Answer 3

what ?

Answer 4

please wait, I'm working on your question...

Answer 5

okay...

Answer 6

here is my reasoning:

we have:
\[\Large L = 2r\sin x\]

Answer 7

thank you...

Answer 8

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

Answer 9

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

Answer 10

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

Answer 11

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:
\[\large arc(BC) = 2xAB\]

Answer 12

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

Answer 13

brilliant!

Answer 14

thanks!! :) @alekos

Answer 15

thanks @Michele_Laino

Answer 16

:) @yajna

Answer 17

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

Answer 18

@Michele_Laino is a genius @alekos

Answer 19

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.

Answer 20

A true genius she is! @Michele_Laino :)

Answer 21

yes...

Answer 22

thanks! @Miracrown

Answer 23

@michele what do you do for a living?

Answer 24

at the moment I have no job!

Answer 25

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

Answer 26

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

Answer 27

from English to Italian

Answer 28

and my preceding job was nautical draughtsman

Answer 29

have you been out of work for long?

Answer 30

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

Answer 31

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

Answer 32

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