Problem I could not figure out.

[Aquib]

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.

[Hasib]

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

[Moon]

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.

[Zzzz]

Edited the first post.

[Tahmid Hasan]

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

[Tahmid Hasan]

disproved,won't work in the case of tan90!!!!!!!11