Question

In the trapezoid ABCD ( AB ∥ CD ) point M∈ AD , so that AM:MD=3:5. Line l ∥ AB and going trough point M intersects diagonal AC and leg BC at points P and N respectively. Find: BC:BN

Answer 1

BC : BN = 8 : 3

Explanation:

Parallel lines divide any transversal into segments with the same ratio. That means ...

... BN : NC = AM : MD = 3 : 5

Since BC = BN + NC, the desired ratio is ...

... BC : BN = (BN+NC) : BN = (3+5) : 3

... BC : BN = 8 : 3