You know you have to learn something new everyday to make up for all the stuff you are going to forget.
You know you have to learn something new everyday to make up for all the stuff you are going to forget.
True, but I think I'm forgetting a lot faster than that will make up for.
You should keep the brain active as a lot of study's have shown. You can do this (one way) by doing
Dave Lindell's great problems he comes up with.
The GeoGebra online grapher looks suspiciously similar to the intersection of a sewer and a drainage system I was asked to stake out. I couldn't figure that out either. ?ÿ
Having spent many wee hours deriving test problems, and having published some on tests that weren't solvable, I know that it is a challenging process. The job that Dave does with this is outstanding and he reaches an audience far wider than surveyors. One of his problems many years ago bridged the gaps between geometry, calculus, and the Cartesian coordinate system for one of my AP Calculus classes.
In this case, it's key to get the quadrilateral and its circumscribed circle fixed on the plane. Three points determine a circle, but the vertices of the quadrilateral form four points on a circle. There are four combinations of three points and each of these has to determine the same circle.
If a point, say E, is movable, then the circumscribed circle can indeed remain the same, but the quadrilateral has to change. The lengths of two sides (EA and EC) change as does the diagonal AC.
That changes the size and location of the inscribed circle. Perhaps one more given will do the trick, or some clever way to solve for that potential given. It's definitely a challenge.
I had a vague recollection of Ptolemy's theorem, but I did have to look it up. Given that so many shapes in the real world are irregular, it really should get more than a passing note in geometry classes, but time is critical, so most it is devoted to regular polygons.
I drew it in CAD and this is what I came up with.
To create the small circle, I did a 3 point circle and used the Tangent snap to pick the 2 lines and larger circle.
That looks good. The final test is this: are the lengths of the two tangent lines from their intersection to their points of tangency equal?
Geogebra is not quite sophisticated enough to do the circle, but a cut-and-fit approach gets very close to yours.