Guys I have a problem.I couldn't figure it out.Hope you guys can help me.
Let ABC be a triangle such that the coordinates of the points A and B are rational numbers.Prove that the coordinates of C are rational if and only if tanA,tanB and tanC,when defined,are all rational numbers.
Thanks.
Aquib.
Problem I could not figure out.
Re: Problem I could not figure out.
Plz, dont write text in the dollar sign. U also may use the code \text{your text}. Such as x^2 \text{ means to multiple the x twice} will give u $x^2 \text{ means to multiple the x twice}$ thanks
A man is not finished when he's defeated, he's finished when he quits.
Re: Problem I could not figure out.
In general don't use LaTeX where you can simply write it with your keyboard. However, you may write something like $ABC$ with LaTeX codes, because it is part of the mathematical symbols we are using.
"Inspiration is needed in geometry, just as much as in poetry." -- Aleksandr Pushkin
Please install LaTeX fonts in your PC for better looking equations,
learn how to write equations, and don't forget to read Forum Guide and Rules.
Please install LaTeX fonts in your PC for better looking equations,
learn how to write equations, and don't forget to read Forum Guide and Rules.
Re: Problem I could not figure out.
Edited the first post.
Every logical solution to a problem has its own beauty.
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(Important: Please make sure that you have read about the Rules, Posting Permissions and Forum Language)
- Tahmid Hasan
- Posts:665
- Joined:Thu Dec 09, 2010 5:34 pm
- Location:Khulna,Bangladesh.
Re: Problem I could not figure out.
let's assume that the co-ordinate of point C is rational.so the value of $$AB,BC,CA$$ is rational.so the area of $$\Delta ABC$$ is rational.
now $$tan A=\frac{4\Delta}{(b^2+c^2-a^2)}$$ is rational.the others tans can also b proved like this.
contradiction can be used to solve the other part.
plz notify if i'm wrong
now $$tan A=\frac{4\Delta}{(b^2+c^2-a^2)}$$ is rational.the others tans can also b proved like this.
contradiction can be used to solve the other part.
plz notify if i'm wrong
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- Tahmid Hasan
- Posts:665
- Joined:Thu Dec 09, 2010 5:34 pm
- Location:Khulna,Bangladesh.
Re: Problem I could not figure out.
disproved,won't work in the case of tan90!!!!!!!11
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