Kirk Braunius


Assignment 7: Tangents


Problem:  Construct a tangent line to a given circle passing through a given point outside the circle. Euclid's solution to this problem is demonstrated using GSP.


Start with circle C2 with center E, and point A.  We want a line through A and tangent to C2.

Construct line AE, then point D at the intersection with C2. Construct line j through D and perpendicular to AE.Construct circle C1, center at E and radius AE.

Construct point F at the intersection of j and C1.Construct line EF, then point B at the intersection of EF and C2.

Construct line AB.

Now triangle AEB is congruent to triangle FED by SAS (they share angle E, FE = AE, and DE = BE).By definition, angle FDE is 90 degrees, so angle ABE is 90 degrees and AB is tangent to C2.