Curriculum placement
Geometry. This describes the skill, not a learner estimate.
A tangent from a point outside a circle
Construct tangents from an exterior point and justify perpendicular radii
Problem types
- Compute with tangents to a circle
- The steps of the tangent construction
- Justify the tangent construction
Builds on
- Theorems about circles
- Constructions with compass and straightedge
- Slopes of parallel and perpendicular lines · Useful idea
A tangent is perpendicular to the radius at the point of tangency, and perpendicular lines have slopes whose product is -1.
- How many times a line meets a curve · Useful idea
A line that meets a circle in exactly one point is tangent to it, which the count of intersections detects.
Leads to
- Equations of circles · See it applied
The tangent at a point of a circle is perpendicular to the radius to that point, so its slope is the negative reciprocal of the radius slope.
- Conic sections and their equations · Extend the idea
A tangent to a conic touches it at one point, extending the tangent to a circle to ellipses, parabolas and hyperbolas.
- Vectors and their components · See it applied
A tangent is perpendicular to the radius, which is a dot product of zero between the tangent vector and the radius vector.
Related skills
- The incircle and the circumcircle · Related idea
The incircle of a triangle is tangent to all three sides, and each radius to a point of tangency is perpendicular to that side.
- Regular polygons inscribed in a circle · Shared foundations
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