In an equilateral triangle ΔABC, D divides BC in the ratio 2 : 1 while E divides AC in the ratio 1 : 2. Find BE : ED.
Let the side of the equilateral triangle ΔABC be 3 units. Clearly, BD = 2, CD = 1 and CE = 2.
CD/CE = ½. So <DEC=30°
Hence, ΔCDE is a right angled triangle.
Similarly, ΔBDE is also a right angled triangle.