Yesterday I was talking to a guy on discord about AGI. Together we tested the new version of gpt 3. But I did not prepare for this discussion, I did not expect that I would need to formulate questions for AI. I asked some stupid questions about the Titanic, largest prime number and halting problem. But now I have prepared interesting problems from the book and one problem for knowledge of physics, namely the knowledge of the Coriolis force. You can view the tasks at this link.
# This challenges taken from the book "Challenging Problems in Geometry"
It dont require any additional drawings, only the text description.
I assume that gpt3 system on 3 december 2022 does not take any images as an input query.
[download the book "Challenging Problems in Geometry" Posamentier, Alfred, S_Salkind, Charles](https://github.com/Kvazikot/BallPark/raw/main/(Dover%20Books%20on%20Mathematics)%20Posamentier%2C%20Alfred%2C%20S_Salkind%2C%20Charles%2C%20T%20-%20Challenging%20Problems%20in%20Geometry-Dover%20Publications%20(2012).mobi)
0. simple!
What is the surface area of the following cone radius of the base is 2 the height is 6 ?
1. If the point were on the extension of a side of the rectangle, would the result still hold?
2. The measure of the longer base of a trapezoid is 97. The measure of the line segment joining the midpoints of the diagonals is 3. Find the measure of the shorter base.
3. In parallelogram ABCD, points E and F are chosen on diagonal AC so that AE = FC. if BE is extended to meet AD at H, and BF is extended to meet DC at G, prove that HG is parallel to AC.
4. Two telephone cable poles, 40 feet and 60 feet high, respectively, are placed near each other. As partial support, a line runs from the top of each pole to the bottom of the other. How high above the ground is the point of intersection of the two support lines?
5. Find the measure of the shorter secant if the measure of the angle between the secants is 45
6. Two circles intersect in A and B, and the measure of the common chord AB is 10. The line joining the centers cuts the circles in P and Q. If PQ = 3 and the measure of the radius of one circle is 13, find the radius of the other circle.
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