Advanced query (Plus mode)

Advanced query relates an object to auxiliary poins derived from a declared subset  ob objects in a configuration.

Given a configuration, OK Geometry provides a list of observed properties. With subsequent query buttons (magenta coloured buttons on the right hand side of the displayed construction, e.g. ?⚫, ?△ ) you ask OK Geometry to show only properties that contain a given object. 

In Plus mode, the query buttons have an additional functionality: in a configuration it tries to relate a specified object to a specified subset of objects in a configuration, and also to many objects geometrically derived from the specified subset of objects.

The advanced query is a great help for hypothetising solutions to construction tasks. It also brings to light surprising new relations among objects in a configuration.

Let us illustrate the use of advanced query with a very simple example:


How to inscribe a square PQRS into a given triangle, as shown in the figure?

First, we need to obtain a configuration - the easiest way is to start with a square PQRS and draw an appropriate triangle ABC around it.

In our initial construction task the given object are the vertices A,B,C and the three sides of the triangle. The non-given objects are the vertices P,Q,R,S and the four sides of the triangle.
We mark the non-given objects using the green ⚫?  button. The non-given points become pale green, and the non-given lines turn dashed and pale green.

At this point we Observe the configuration and obtain the usual list of properties of the configuration. On the very right of the display the query buttons appear (magenta coloured buttons on the right hand side of the displayed construction, e.g. ?⚫, ?△, These button are used to query specific objects. 
 
For example, with the query point button ?⚫ we query the point R. After a while a short list of properties involving the point R appears. At the end of the list you may find new properties that involve auxiliary points derived from known objects. A click on the property displays the property.

For example: The property Lines invoving R contains, among other, the property R, _360, _353 (Note that you may get different numbers with underscore for the same auxiliary points.) 

If you put the cursor on an auxiliary point, an explanation of the point appears (you can activate the visual explanation with F8 button). In the shown example _360 is the orthogonal projection of C onto the line AB, and the point _353 is the point A rotated clockwise around B by 90 degrees.

As usual, with the commands in right-click menu you can export the figure or edit it and include it in a project. In this case the underscores in labes turn into Y.  
To obtain information about the point Q, just apply the query point command ?⚫ on the point Q (no need to observe again). Here it is shown a property that allows the construction of point Q (the auxiliary point _280 is the point A rotated anticlockwise around B by 90 degrees).

Both properties we mentioned are easy to be proved.

Note. A change in the collection of non-given objects requires a new observation.



You can find more examples of the use of advanced query here.