Application of Zhongwang CAD2009 to the vertical point in the three-point circle method

And sometimes the relationship at this particular location is more subtle, which requires us to explore hidden conditions from known conditions.
Let's take a look at an example. Through this example, we will master the application of Zhongwang CAD 2009 in the three-point circle method. The example is: Find the radius of the red arc based on known conditions.

Known conditions: the line segment length is 10, the angle with the horizontal direction is 60°, one end point is at the point (25, 20); the known circle diameter is 30, and the center of the circle is at the point (50, 60).
Find: the radius of the red arc. (The red arc is tangent to the line and the circle, and the end point above the line segment 10)
First of all, analyze this topic. It is known from the topic that the arc to be obtained is tangent to the line segment and the known circle. Therefore, it is easier to think of the tangent, tangency, and tangent circle method of Zhongwang CAD2009. But there are only two objects that are tangent to it. Take a closer look at "and the end point above the line segment 10", indicating that the tangent point of the arc and the line segment is the upper end point, and then know that the center of the arc is definitely perpendicular to the line segment 10 and above the end point. On the vertical line, you can do the vertical line BC. Then, using BC as the mirror line to mirror the known circle, the third tangent target is obtained. At this time, it is natural to use the tangent, tangency, and tangent circle method. Figure:

Finally, the excess part is trimmed and deleted, and the radius of the arc is 43.34.
The second method is to use the three-point circle method, which is also a method I want to focus on in this article. It is known from the known two points: the tangent point of the known circle and the end point of the line segment. So there is one point, and the most important one, how to find it? It is said that the center of the circle is definitely on the vertical line BC, so we can use the foot to capture the BC line to get the third point. Figure:

The three points are also clearly identified in the figure. Obviously, for this example, the three-point circle method is more convenient than the tangency, tangency, and tangency methods, because there is no need to mirror auxiliary steps such as known circles.
In the past, when I used three points to draw a circle, I basically thought that there must be three points that were circled. I believe many people will think so. However, through this example, we will find that: with the practical function of Zhongwang CAD2009, in fact, as long as there are two points, we can determine the line where the center of the circle is located (that is, the third point is obtained by capturing the line where the center of the circle is located), and can also use three. Draw a circle method to draw a circle.
I hope this article will make everyone realize the practical performance of Zhongwang CAD 2009, and realize that using Zhongwang CAD2009, "Danging Point" is a very useful feature point in the three-point drawing circle method.

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