How to prove that line segment BF=tan x.tan y?

[Kamalesh]

Homework Statement

I came across a problem in geometry I don't know how to prove BF so please help me ?

Relevant Equations

Prove BF =tan x.tan y

 

[mitochan]

Hello.
How do you estimate BD? Then how do you estimate BF by BD?

 

[Mark44]

How do you estimate BD? Then how do you estimate BF by BD?

The problem doesn't require any estimation.

@Kamalesh, in your work you have several lines such as "$BD \Rightarrow \tan y$" and others. The arrow symbol means "implies." You should be using "equals" (=) instead.

Triangles ABC and BDF are similar triangles, which means that their corresponding sides are proportional. In this case side BC in the left triangle corresponds to side BF in the right triangle. Set up a proportion using these two sides and two other corresponding sides of the triangles, and the result pops out quickly

 

[archaic]

Observe $\mathrm{DBF}$, it looks like you can express $\mathrm{BF}$ as a function of $x$.
The problem here is that you went and found an expression for everything except what you're looking, $\mathrm{BF}$ that is.

 

[neilparker62]

Find expressions for tan(x) and tan(y) and simply multiply them.