Enigma 1167: Christmas lines
From New Scientist #2322, 22nd December 2001 [link]
With the help of my niece and nephew I have designed my own Christmas Card this year. We started with a large rectangular piece of card and then near to the top left-hand corner we drew a red dot and a gold dot representing two baubles. Then I wanted to draw a line through at least one of the baubles to create a triangle in that corner of the card.
Linus suggested we draw the line through the red bauble in the direction which made the line as short as possible. Tynia said to draw the line through the gold bauble in the direction which made the area of the triangle formed as small as possible. As a compromise we decided to draw the line through both baubles.
Luckily this line satisfied both Linus’s and Tynia’s requirement. It was 20 cm long and the triangle formed had an area of 80 cm².
How far apart were the two baubles?