Florida B.E.S.T. MA.912.GR.5.5

MathGrades 9–12Make formal geometric constructions with a variety of tools and methods.

The Standard

Given a point outside a circle, construct a line tangent to the circle that passes through the given point.

Florida B.E.S.T. Standards for Mathematics

Teacher's field guide

What Students Need to Do: Students use a compass and straightedge or geometry software to construct a tangent from an outside point to a circle. They justify the construction using a radius perpendicular to the tangent.
What Mastery Looks Like: Students accurately construct either tangent line and keep the compass marks that show their method. They explain that the radius to the contact point is perpendicular to the tangent.
Common Misconceptions: Students may draw a line that looks tangent without constructing or proving the contact point. They may make the tangent perpendicular to the wrong segment or miss that two tangent lines are possible.
How to Assess It: Exit ticket: Given a circle with center O and an outside point P, construct one tangent through P. Leave all construction marks and label the right angle.

Lesson moves

With a compass and straightedge, connect the center to the outside point, bisect that segment, then use the midpoint circle to locate tangency points.
Write why each intersection of the original circle and the circle with diameter OP creates a right angle and a tangent.
Run a construction relay where pairs complete one step, pass the diagram, and check each finished tangent with a right angle tool.
Model a straight road touching a circular fountain from an outside gate, then construct the road’s path without crossing the fountain.

Keep exploring

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