What is the ratio of $\frac {BK}{BE}$?

Question

Here is my diagram

Here is what are given

$$|BD| = 2$$ $$|DC| = 5$$ $$|AE| = 2$$ $$|EC| = 3$$

• What is the ratio of $\frac {BK}{BE}$?

I'm so confused right now.

Answer 1

If you follow the construction I made in my picture below, it's easy to see that $BK=KE$ and therefore $\frac{BK}{KE}=1$

Answer 2

Raffaele your statement that BK = KE is true, but the question asked for the ratio of BK to BE. Your diagram appears to be correct, but you set up the wrong ratio. So, the correct ratio of BK/BE is 2/4, or 1/2.