### In a triangle, ABC, D is a point on AB such that AB = 4AD and E is a point on AC such that AC = 4AE. Prove that BC = 4ED.

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**Answer: **

**Step by Step Explanation: **- It is given in the question that D and E are the points on side AB and BC of ΔABC respectively. Join DE.

**Given:-** AB = 4AD

or, AD = AB

AC = 4AE

or, AE = AC- We need to prove that the ΔADC and ΔABC are similar.

Where, A is the common angle in ΔADE and ΔABC.

Therefore, = **[By BPT theorem.]**

Then, = = ------(1)

So, ΔABC ∼ ΔADE **[By SAS criteria.]** - As, = ------(2)

and = ------(3) - On comparing (1), (2) and (3), we get:
=

- Hence, BC = 4ED.