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

BC:BN=8:3

Step-by-step explanation:

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

let's fu(!

step-by-step explanation: