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.

1. For the given Trapezoid ABCD the value of BC:BN is BC:BN=8:3.
What is Trapezoid?
A trapezoid is a quadrilateral in American and Canadian English that has at least one pair of parallel sides. A trapezium is the term used in British and other varieties of English. In Euclidean geometry, a trapezoid is invariably a convex quadrilateral. The trapezoid’s parallel sides are referred to as its bases.
Given:
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.
We have to find BC:BN
ABCD is a trapezoid and there is a point m which belongs to AD such that AM:MD=3:5.Line “l” parallel to AB intersects the diagonal AC at p and BD at N.
Now, we know that the parallel lines divide the transversal into the segments with equal ratio, therefore, BN:NC=AM:MD
But, BC= BN+NC
Therefore, BC:BN = (BN + NC): BN
⇒ BC:BN = (3 + 5): 3
⇒ BC:BN = 8:3
Hence, for the given Trapezoid ABCD the value of BC:BN is BC:BN=8:3.