# construction of tangent

Task. Using the compass and straightedge, construct to a given circle the tangent lines through a given point outside the circle.

Let $O$ be the centre of the given circle and $P$ the given point. With $OP$ as diameter   , draw the circle (see midpoint    ). If $A$ and $B$ are the points where this circle intersects the given circle, then by Thales’ theorem, the angles $OAP$ and $OBP$ are right angles   . According to the definition of the tangent of circle, the lines $AP$ and $BP$ are required tangents.

The convex angle $APB$ is called a tangent angle (or tangent-tangent angle) of the given circle and the convex angle $AOB$ the . It is apparent that a tangent angle and the corresponding central angle are supplementary.  The chord $AB$ is the tangent chord corresponding the tangent angle and the point $P$ (see equation of tangent chord (http://planetmath.org/EquationOfTangentOfCircle)!).

The tangent angle is the angle of view of the line segment $AB$ from the point $P$.

 Title construction of tangent Canonical name ConstructionOfTangent Date of creation 2013-03-22 17:36:04 Last modified on 2013-03-22 17:36:04 Owner pahio (2872) Last modified by pahio (2872) Numerical id 15 Author pahio (2872) Entry type Algorithm Classification msc 51M15 Classification msc 51-00 Related topic Incircle  Related topic AngleBisectorAsLocus Defines tangent angle Defines tangent-tangent angle Defines tangent chord