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A line DE parallel to BC (D on AB, E on AC) divides triangle ABC into two parts of equal area. What is AD : DB?

Competition practiceGeometry

A(√2 + 1) : 1
B1 : 1
C√2 : 1
D1 : (√2 + 1)

Step-by-Step Solution

(\frac{A D}{A B})^{2} = \frac{1}{2}

, so

A D : A B = 1 : 2

and

A D : D B = 1 : (2 - 1) = (2 + 1) : 1

.

Answer: A) (√2 + 1) : 1

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