What a Tangent Is
Part of the Circles section of Coddy's Geometry journey. Lesson 47 of 62.
A tangent is a straight line that touches a circle at exactly one point, the point of contact, without crossing into it. A line that cuts through the circle at two points is not a tangent.
The tangent always meets the radius at the point of contact at 90°. Here is why. Every other point of the tangent line is outside the circle, so it is farther from O than T is. T is the closest point of the line to the center, and the shortest path from a point to a line is the one at right angles to it. The rule is called Tangent and radius.
Challenge
OT is a radius of circle O. Drag the point P until the segment TP is a tangent to the circle at T, then press Check.
Try it yourself
Drag the figure and watch
Test yourselfThis lesson includes a short quiz. Start the lesson to answer it and track your progress.
All lessons in Circles
1Parts of a Circle
Center and RadiusChords and DiametersAll Radii Are EqualDiameter Is Two RadiiRecap: Parts of a Circle4Arcs and Sectors
Arc LengthArea of a SectorFind the Central AngleThe Missing Central AngleRecap: Arcs and Sectors7Angles in a Semicircle
Thales' TheoremThe Right Angle InsideIs That Enough?Semicircle With LettersRecap: Semicircles10Tangents
What a Tangent IsTangent and RadiusTangent LengthsTwo Tangents From a PointTangents With LettersRecap: Tangents2Circumference
Around the CircleUsing the DiameterRadius From CircumferenceCircumference With LettersRecap: Circumference5Radii Make Isosceles
Two Radii, One TriangleBase Angles From the CenterThe Angle at the CenterIsosceles With LettersRecap: Radii and Triangles8Angles on the Same Arc
Same Arc, Same AngleUsing the Same ArcSpot the Bow TieSame Arc With LettersRecap: Same Arc3Area of a Circle
The Area FormulaArea From the DiameterRadius From the AreaCircumference to AreaRecap: Area of a Circle6Inscribed Angles
Meet the Inscribed AngleHalf the Central AngleTwice the Inscribed AngleThe Big ArcInscribed With LettersRecap: Inscribed Angles