In the problem does not specify where exactly should be the point. Draw it right on the circle and not inside it - and a formal decision is made.
Try the inaccuracy in terminology. The condition uses the term "circle" instead of "circumference". Unlike the circle, the circle is solid. Draw it, then put inside it the bullet. This can be done without lifting your pencil from the paper.
In the problem statement does not say whether to use the second pencil. Also not specified how many pencils can not be separated from the paper. Draw a dot inside the second circle with a pencil, without lifting off paper first.
The problem statement does not contain information about whether the circumference to connect to a point inside the line. Assuming that the drawing of such a line is not prohibited, draw a circle, and then, without lifting your pencil from the paper, draw a line inside it, and then draw a point. Moreover, because the condition does not say definitely whether the point should be inside the circle, try to draw it outside.
Being a true formalist, to solve this problem. Since in the condition they say it is the pencil, not the pen, the pen, press it onto the paper, the pencil, and then, without lifting it, draw another drawing tool, a circle and a point inside it.
The condition is not stated which part of the pencil can not be separated from the paper. Press to the sheet (same or different - in condition nothing is said on this subject) the opposite side of the pencil and the pen, draw a circle and a point with margin.
Draw a circle with a compass. Dot in its center will turn itself. Since the compass includes a pencil, formally, the task is considered solved.
Finally, the most elegant way of solving this problem is the following. Draw a circle, then fold the corner of the paper along with a pencil, without lifting it, so that the stylus touched the paper with the reverse side in the center of the circle. Then pierce the paper with a stylus.
If forum trolls will tell you in response that none of the proposed solutions to the problem is not correct, please provide your counter. It is as follows: to solve the problem is impossible, because after a circle with a dot is drawn (regardless of how), the pencil will have the paper to tear, and the condition of the problem forbids it. Do not glue it. But better to remember the famous advice: "don't feed the trolls".