Here you go...

It looks like the math pans out.  In this image, the values higher on the image are the distances between the vertex A and the green intersection vertices 1,2 and 3.  The values below them are the distances from vertex A to the line B-C along the lines through A-1, A-2 and A-3, represented by the blue dots at the bottom.  Here's the 3 computed weights...

0.385427170553870397511318682665 = 1.0 - (150.539 / 244.949 = 0.61457282944612960248868131733545)
0.385431156655401722446309822305 = 1.0 - (140.936 / 229.325 = 0.61456884334459827755369017769541)
0.385430688663592821333858063478 = 1.0 - (137.422 / 223.607 = 0.61456931133640717866614193652256)

...note that the weights are all the same (within 4 decimal places... the software only gave me 3 decimal places of measurement).  So the weighting for A for each intersection point 1,2 and 3 would all be the same.

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