# NavList:

## A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding

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Re: Christmas week Quizzes
From: David Pike
Date: 2020 Dec 30, 02:05 -0800

The solution to Quiz 3 is below. There are other ways to put the vectors together so long as you get to the correct place in the end.  Well done Modris our results are very close.

Quiz No 5
Unfortunately, while I was going over Quiz 3 in ink, my clever cousin Cedrick got hold of my geometry set and started playing around with it.
First, he used it to construct an equilateral triangle of side 10cm.  Then he asked me to find the maximum number of points I could pick so that each pair of points is more than 5cm apart.  He let me use the three corners of the triangle as three of my points.  How many points can you find?

Next on a fresh sheet of paper, he drew three circles at random.  He then drew the common external tangents to each pair of circles as in the diagram below. Finally, he extended each pair of tangents until they crossed and asked me to explain to him as simply as possible why the three points were colinear.  My answer of ‘By magic’ didn't satisfy him.  How would you explain it to him? DaveP

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