A Tangent From a Point
Part of the Transformations & Constructions section of Coddy's Geometry journey. Lesson 55 of 61.
A tangent touches a circle at one point and meets the radius there at a right angle. To draw one from an outside point P, you need the point T on the circle where ∠OTP is 90°.
The rule Angle in a semicircle finds it. Take the midpoint M of OP and draw the circle about M through O, which has OP as a diameter. Any point of that circle other than O and P makes a right angle with O and P. Where it crosses the given circle is T: then ∠OTP = 90°, so PT meets the radius OT at right angles and touches the circle.
Challenge
Construct a tangent to the circle from the point P, then press Check. The Midpoint tool is unlocked.
Try it yourself
Construct it with a compass and straightedge
Test yourselfThis lesson includes a short quiz. Start the lesson to answer it and track your progress.
All lessons in Transformations & Constructions
7Drawing on Squared Paper
Lengths by PythagorasPerpendicular StepsSquares by AreaRight Triangles by AreaMidpoints on the GridRecap: Squared Paper10Perpendiculars and Parallels
Perpendicular From a PointPerpendicular at a PointParallel Through a PointTools You Have EarnedRecap: Parallels5Dilations
Scaling From a CenterShrinking a ShapeDilating About a PointNegative Scale FactorsRecap: Dilations8Compass and Straightedge
Circles Keep DistancesWhy the Sides MatchAngles You BuiltA 60° AngleRecap: Equilateral Triangle11Constructed Shapes
A Square on a SegmentThe Regular HexagonCopy an AngleA Tangent From a PointRecap: Constructed Shapes