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Constructing Tangent Lines

Constructing Tangent Lines. Adapted from Walch Education. Key Concepts. If a line is tangent to a circle, it is perpendicular to the radius drawn to the point of tangency, the only point at which a line and a circle intersect. Exactly one tangent line can

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Constructing Tangent Lines

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  1. Constructing Tangent Lines Adapted from Walch Education

  2. 3.3.1: Constructing Tangent Lines Key Concepts • If a line is tangent to a circle, it is perpendicular to the radius drawn to the point of tangency, the only point at which a line and a circle intersect. • Exactly one tangent line can be constructed by using construction tools to create a line perpendicular to the radius at a point on the circle.

  3. 3.3.1: Constructing Tangent Lines

  4. 3.3.1: Constructing Tangent Lines

  5. 3.3.1: Constructing Tangent Lines Key Concepts, continued • If two segments are tangent to the same circle, and originate from the same exterior point, then the segments are congruent.

  6. 3.3.1: Constructing Tangent Lines

  7. 3.3.1: Constructing Tangent Lines

  8. 3.3.1: Constructing Tangent Lines

  9. 3.3.1: Constructing Tangent Lines Key Concepts, continued • If two circles do not intersect, they can share a tangent line, called a common tangent. • Two circles that do not intersect have four common tangents. • Common tangents can be either internal or external.

  10. 3.3.1: Constructing Tangent Lines Key Concepts, continued • A common internal tangent is a tangent that is common to two circles and intersects the segment joining the radii of the circles.

  11. 3.3.1: Constructing Tangent Lines Key Concepts, continued • A common external tangent is a tangent that is common to two circles and does not intersect the segment joining the radii of the circles.

  12. 3.3.1: Constructing Tangent Lines Practice Use a compass and a straightedge to construct tangent to circle A at point B.

  13. 3.3.1: Constructing Tangent Lines Draw a ray from center A through point B and extending beyond point B

  14. Put the sharp point of the compass on point B. Set it to any setting less than the length of , and then draw an arc on either side of B, creating points D and E.

  15. Put the sharp point of the compass on point D and set it to a width greater than the distance of . Make a large arc intersecting .

  16. Without changing the compass setting, put the sharp point of the compass on point E and draw a second arc that intersects the first. Label the point of intersection with the arc drawn in step 3 as point C.

  17. Draw a line connecting points C and B, creating tangent . • Do not erase any of your markings. • is tangent to circle A at point B.

  18. 3.3.1: Constructing Tangent Lines Try this one… Use a compass and a straightedge to construct the lines tangent to circle C at point D.

  19. Thanks for Watching ~Ms. Dambreville

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