Question

In the given figure, DE || AC, DC || AP, BC = 2 cm, and BP = 6 cm. Find the value of EC/BE.

Answer 1

Solution:

In △BPA, we have DC∣∣AP [Given]
Therefore, by basic proportionality theorem, we have

𝐵𝐶/𝐶𝑃=𝐵𝐷/𝐷𝐴……(𝑖)

Similarly, in △BCA, we have DE∣∣AC.
Therefore, by basic proportionality theorem, we have

𝐵𝐸/𝐸𝐶 = 𝐵𝐷/𝐷𝐴……(𝑖𝑖)​

From (i) and (ii), we get

𝐵𝐸/𝐸𝐶 = 𝐵𝐶/𝐶𝑃…….(𝑖𝑖𝑖)

​We have BP = BC + CP

So, CP = 6−2 = 4 𝑐𝑚

We can write equation (𝑖𝑖𝑖) as

𝐸𝐶/𝐵𝐸 = 𝐶𝑃/𝐵𝐶

Putting the values of CP and BC , and we get

𝐸𝐶/𝐵𝐸 = 4/2 = 2