Question

draw a tangent to a circle parallel to a given straight line
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Answer 1

This shows how to construct the tangent to a circle at a given point on the circle with compass and straightedge or ruler. It works by using the fact that a tangent to a circle is perpendicular to the radius at the point of contact. It first creates a radius of the circle, then constructs a perpendicular to the radius at the given point.The image below is the final drawing above.

Argument Reason

1 Line segment OR is a radius of the circle O. It is a line from the center to the given point P on the circle.

2 SP is perpendicular to OR By construction, SP is the perpendicular to OR at P. See Constructing a perpendicular to a line at a point for method and proof.

3 SP is the tangent to O at the point P The tangent line is at right angles to the radius at the point of contact. See Tangent line definition