Math CentralQuandaries & Queries


Question from elizabeth, a student:

show that the radius of a circle meets a tangent line to the circle in a 90 degree angle.
hint: start by assuming they are not perpendicular and at a contradiction.

Hi Elizabeth,

Suppose that PQ is a diameter of a circle and construct the tangent line to the circle at P. Construct a line from Q to meet the tangent line at R.


If the tangent line does not make a right angle with the diameter QP then P and R are different points. Since QP is a diagonal to the circle and angle PRQ is a right angle, what can you say about the point R?


About Math Central


Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.
Quandaries & Queries page Home page University of Regina PIMS