EngageNY
Equations for Tangent Lines to Circles
Don't go off on a tangent while writing equations of tangent lines! Scholars determine the equations for tangent lines to circles. They attempt both concrete and abstract examples, such as a tangent line to the unit circle through...
Curated OER
Tangent Lines and the Radius of a Circle
Your Geometry learners will collaboratively prove that the tangent line of a circle is perpendicular to the radius of the circle. A deliberately sparse introduction allows for a variety of approaches to find a solution.
Texas Instruments
Drawing a Line Tangent to a Circle
Explore lines tangent to a circle. In this math lesson plan, students manipulate circles and lines on a TI calculator. They draw a circle and analyze perpendicular lines intersecting the circle in only one place. This activity...
EngageNY
Tangent Lines and the Tangent Function
Construct tangent lines and make the connection to tangent functions. An informative lesson reviews the geometry origins of the tangent function. Pupils use that information to determine how to construct a tangent to a circle from a...
EngageNY
Properties of Tangents
You know about the tangent function, but what are tangent lines to a circle? Learners investigate properties of tangents through constructions. They determine that tangents are perpendicular to the radius at the point of tangency,...
EngageNY
The Inscribed Angle Alternate – A Tangent Angle
You know the Inscribed Angle Theorem and you know about tangent lines; now let's consider them together! Learners first explore angle measures when one of the rays of the angle is a tangent to a circle. They then apply their...
EngageNY
Why Call It Tangent?
Discover the relationship between tangent lines and the tangent function. Class members develop the idea of the tangent function using the unit circle. They create tables of values and explore the domain, range, and end behavior of...
Illustrative Mathematics
Two Wheels and a Belt
Geometry gets an engineering treatment in an exercise involving a belt wrapped around two wheels of different dimensions. Along with the wheels, this belt problem connects concepts of right triangles, tangent lines, arc length, and...
EngageNY
Tangent Segments
What's so special about tangents? Learners first explore how if a circle is tangent to both rays of an angle, then its center is on the angle bisector. They then complete a set of exercises designed to explore further properties and...
EngageNY
Similar Triangles in Circle-Secant (or Circle-Secant-Tangent) Diagrams
First angle measures, now segment lengths. High schoolers first measure segments formed by secants that intersect interior to a circle, secants that intersect exterior to a circle, and a secant and a tangent that intersect exterior to a...
Texas Instruments
Exploring Tangents
Explore the concept of tangent lines. In this tangent line lesson plan, learners graph a circle and two lines on their graphing calculator using Cabri Jr. Students construct the lines so that they both intersect at a given point and are...
Virginia Department of Education
Angles, Arcs, and Segments in Circles
Investigate relationships between angles, arcs, and segments in circles. Pupils use geometry software to discover the relationships between angles, arcs, and segments associated with circles. Class members use similar triangles to...
EngageNY
Secant Lines; Secant Lines That Meet Inside a Circle
Young mathematicians identify different cases of intersecting secant lines. They then investigate the case where secant lines meet inside a circle.
Curated OER
Tangent Properties
Students explore properties of tangent lines. In this properties of tangent lines activity, students discuss the perpendicular relationship between a tangent line on a circle and the circle's radius. Students use that...
Curated OER
Secant Line Approximation of the Tangent Line
Students perform operation with secant and tangent lines. In this calculus lesson, students find the derivative and relate it to the slope of a line. They differentiate between secant and tangent as they intersect a circle, using Cabri.
Mathematics Assessment Project
Inscribing and Circumscribing Right Triangles
High schoolers attempt an assessment task requiring them to find the radii of inscribed and circumscribed circles of a right triangle with given dimensions. They then evaluate provided sample responses to consider how to improve...
Curated OER
Tangents to a Circle
Young scholars construct tangent lines. In this geometry instructional activity, students identify the point of tangency, secant and tangent lines. They graph the lines on the Ti and make observations.
Curated OER
Circles and Angles
Students identify tangents, chords and secants. In this geometry lesson, students graph circles and identify angles created by secant lines, tangent lines and chords.
Curated OER
Intersecting Lines and Segments of Measures
Mathematicians measure intersecting lines-and circles, and create chords. In this geometry activity, students explore interrior and exterior chords created by tangent and secant lines. These segments can be inside the circleor outside...
Curated OER
Circle Conjectures
Students are given diagrams and are asked to make a conjecture. In this geometry lesson, students make conjectures of circles. They complete a lab activity to reinforce making conjectures. The first activity addresses a common core...
Curated OER
Worksheet 8 - Limit of Slopes
For this limit of slopes worksheet, students compute the limit of slopes, find the slope of the secant line, and determine the slope of the tangent line. This one-page worksheet contains five multi-step problems.
Curated OER
Secants, Tangents and Arcs
Students identify chords and angles. In this geometry lesson, students calculate the length of the chords inside and outside of-the circle. They differentiate between tangent and secant lines.
Curated OER
Circles
Tenth graders explore and define the radius and diameter of a circle. In this geometry lesson, 10th graders calculate the circumference and area of a circle using real world objects and shapes. They discuss chords and lines tangent...
Curated OER
Geometry of Circles - Week 7 (Area & Circumference)
In this circle worksheet, learners solve problems involving the circumference, area and arc length in a circle. They explore the union of circles and semicircles, as well as the line segments tangent to the circle. This two-page...