Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

Using a ruler and a compass how can construct a line through a point and tangent to a circle. What I don't want is to eyeball the line by trying to line-up the ruler over the circle. Best if I could construct the point of intersection first and then draw the line.

PS. I know how to do it mathematically, I just don't know the steps for geometry, given A, C and the circle to find D.

Example

Update Based on answers here is the constructors. Thanks for the quick responses.

Solution

share|improve this question
1  
You could look at mathopenref.com/consttangents.html –  Ross Millikan Oct 29 '12 at 17:39
add comment

3 Answers

up vote 2 down vote accepted

Draw a Thales circle over the segment $AC$, it will intersect the desired $D$, because $AD\perp DC$:

  1. Draw the segment $AC$.
  2. Construct its midpoint $F$.
  3. Draw a circle with origin $F$ and radio $FA(=FC)$.
share|improve this answer
add comment
  1. From AC, find its midpoint F.
  2. Draw the circle using F as center and FA (or FC) as radius.
  3. The point(s) of intersection of the circles is D.
share|improve this answer
    
Thanks, but how is this answer different from the one Berci provided? –  ja72 Aug 12 '13 at 17:30
    
@ja72, Yes but have the extra description cut. –  Mick Aug 22 '13 at 12:56
add comment

Intersect the circle having $AC$ as a diameter with the initial circle: you will find the two points $D,D'$ such that $CD$ and $CD'$ are tangent to the initial circle. This comes from the fact that the circle is the locus of points that "see" any diameter under an angle equal to $\frac{\pi}{2}$.

share|improve this answer
add comment

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.