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## High school geometry

### Course: High school geometry>Unit 8

Lesson 13: Constructing a line tangent to a circle

# Geometric constructions: circle tangent

Sal constructs a line tangent to a circle using compass and straightedge.

## Want to join the conversation?

• Is there anything that relates tan line to tan in trigonometry
• Yes, Kevin, there is a relationship. The length of a line segment that is tangent to a circle AND that connects to a central angle of that circle is the tangent of the central angle.
• Is there an exercise like the one your doing?
• How do you use a compass correctly in real life? Every time I do it, it slides and I can't keep it straight. Any tips?
• I would suggest getting a metal compass and pressing down very hard into the paper where you are drawing. Plastic compasses can slide very easily.
• Something wrong with the order of videos. This should be the first one in the constructing playlist not the last
• Why do the subtitles have <i>P</i> when he says P?
• What are the parametric equations of a circle??
• Parametric equations are a way to show how the progression of a certain scenario, like how a ball travels as it falls from a certain height in a parabola. For the circle specifically, given the equation the circle in standard form, you will have to use trigonometry, which you may or may not have learned.
• how do you access the virtual compass and virtual straight edge?
• how do you draw two tangents to a circle of radius 4cm so that the angle between them is 45degrees??
(1 vote)
• Since tangents are always at 90 degrees to a radius drawn to it, draw any line segment from the center to beyond the line. From any point on the line, you could draw two tangents, So since you want 45 degrees between them, If you divide this in half, you get 22.5 degrees. This would mean you have a right triangle, so find the complement by 90 - 22.5 = 67.5 degrees. So using a protractor, draw an angle with the center as a vertex that is 67.5 degrees, repeat this on the other side of the line you originally drew, and draw a radius using these degrees. This will create the 45 degree angle.
• I used a different method and the exercise didn't recognize it... I used a compass of the same size of the circle on point P, then another compass of the same size that I placed at the intersection of the original circle and my first compass, then drew a straightedge through the center of the circle and the center of the second compass, and then drew a straight edge through the resulting point and P to get a tangent. Why wouldn't that work?!