To construct a secant AB, draw a straight line that intersects the circle at points A and B. For the tangent line p at point C, draw the line so that it touches the circle only at point C and forms a 90-degree angle with the radius OC.
The question asks for the construction of a secant AB and a line p that is tangent to circle O at point C. To answer this, imagine a circle with center O. A secant is a line that intersects the circle at two points. Therefore, draw a straight line such that it cuts through the circle at two distinct points, labeled A and B, respectively. This is your secant AB.
Next, for the tangent line p at point C, identify a point on the perimeter of the circle where you wish this tangent line to touch. The line p should then be drawn such that it touches the circle at just this single point C and does not intersect the circle at any other point. It's important to remember that a tangent to a circle is perpendicular to the radius at the point of tangency. In drawing the tangent line p, ensure that the angle formed by line p and the radius OC is 90 degrees.