In forums, often with the purpose of trolling, the question is asked how to draw a circle with a point, without taking away the pencil from the paper.
In fact, this task has many solutions.
Most of them are based on inaccurate formulation of the problem.
The task does not specify where exactly the point should be located. Draw it directly on the circle, not inside it - and formally the solution is implemented.
Try to take inaccuracies inTerminology. The term "circle" is used in the condition, and not the "circle". Unlike a circle, the circle is continuous. Draw it, and then put a fat point inside it. You can do this without taking the pencil from the paper.
The condition of the task does not say whetherUse the second pencil. Also, it is not specified how many pencils can not be torn from the paper. Draw a point inside the circle with a second pencil, without taking the first one off the paper.
The condition of the problem does not contain information,Can a circle be connected to a point inside it by a line. If you admit that drawing such a line is not forbidden, draw a circle, and then, without lifting the pencil from the paper, draw a line inside it, and then draw a point. Moreover, since the condition does not say whether the point must be inside the circle, try to draw it from the outside.
Being a real formalist, solve this problemCan be so. Since the condition says about the pencil, not the pen, the marker, press the pencil to the paper, and then, without taking it off, draw a circle and a point inside it with another drawing tool.
The condition does not say which part of the pencilCan not be torn from the paper. Press to the sheet (the same or the other - in the condition nothing is said and on this) the opposite side of the pencil, and draw a circle and a point with a lead.
Draw a circle with a compass. The point in its center will turn out itself. Since the compass includes a pencil, the problem will formally be considered solved.
Finally, the most elegant way to solveThis problem is the following. Draw a circle, and then bend the corner of the paper along with the pencil without lifting it, so that the lead touches the paper from the back of the center of the circle. Then puncture the paper with the lead.
In case the forum trolls tell youThe answer is that none of the proposed ways of solving the problem is correct, give your counterargument. It consists in the following: it is impossible to solve the problem at all, since after the circle with the dot is drawn (no matter how exactly), the pencil is still to be torn off from the paper, and this prohibits the condition of the task. Do not glue it. But better remember the famous advice: "Do not feed trolls."