Alignment to Content Standards

CCSS.Math.Content.HSG.CO.D.12
Make formal geometric constructions with a variety of tools and methods (compass and straightedge, string, reflective devices, paper folding, dynamic geometric software, etc.). Copying a segment; copying an angle; bisecting a segment; bisecting an angle; constructing perpendicular lines, including the perpendicular bisector of a line segment; and constructing a line parallel to a given line through a point not on the line.

CCSS.MATH.CONTENT.HSG.C.A.4
(+) Construct a tangent line from a point outside a given circle to the circle.

CCSS.MATH.CONTENT.HSG.CO.A.1
Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point, line, distance along a line, and distance around a circular arc

Tasks

Scheme:

1. Using the above circle A and point B draw segment AB.
2. Construct the Perpendicular Bisector of AB and label the point of intersection M.
3. What is point M in relation to segment AB?
4. What can you say about segments AM and BM?
5. Construct a new circle centered at M with radius BM and label the points of intersection between circles A and M, as Q and R.
6. Draw segments BQ and BR.
7. What can you say about the length of segments BQ and BR? Explain with specifics.

 

Below is the full assignment with answer key

IM Task Tangent to a Circle