Constructing a tangent to a given cirlce from a given point

Euclid III.17
From a given point to draw a straight line touching a given circle

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Given point A and a given circle with center E
Step 1: Draw AE. Get D on the circle
Step 2: Circle center E radius AE
Step 3: Draw a perpendicular line to AE through D. Get F on the bigger circle
Step 4: Draw EF. Get B on the given circle
Step 5: Draw AB.
AB is a straight line touching the given circle!
AB is a tangent line to the given circle!

Emily N. Muhu, Created with GeoGebra