# Solving Semi-circle Inside Triangle Geometry Problem

• mathman
In summary: It is not surprising that it gets things wrong, but it would be nice to see it get things right more often.
mathman
TL;DR Summary
AI cannot do geometry!
Gave following to bing chat and chatgpt, Both gave wrong answers. Any thoughts?
------------------------------
Geometry problem: Semi-circle inside triangle: Triangle with known length sides a, b, c where a is the longest. Place inside the triangle a semi-circle with entire diameter resting on side a, which is horizontal. The arc of the semicircle is maximum possible inside the triangle.
Known - triangle dimensions. Unknown r (semi-circle arc radius) and x (distance along a from left end of a to center of diameter). Find equations for r and x In terms of all possible triangles.

Computer science news on Phys.org
You'll likely need to wait for the Wolfram Alpha plugin to get out of early access for more confident math results.

dsaun777, Wrichik Basu and russ_watters
mathman said:
TL;DR Summary: AI cannot do geometry!

Any thoughts?
Certainly, despite the "AI" claim, ChatGPT doesn't have any.

aaroman, DaveE and russ_watters
There are over a dozen threads here of the form "ChatGPT gets this wrong!" "And this!" "And this too!". To me the surprise isn't that it gets things wrong; it's that it sometimes gets them right.

Maybe it would be best to consolidate all these threads.

aaroman, Demystifier, Motore and 5 others
There are over a dozen threads here of the form "ChatGPT gets this wrong!" "And this!" "And this too!". To me the surprise isn't that it gets things wrong; it's that it sometimes gets them right.
I'd like to say I was surprised by the surprise, but it's easy to get swept up in the hype. After learning the basics of how it works though, I share your take. Maybe when linked to real knowledge sources/tools (like Wolfram Alpha) it will have some reliability.

I detect a similarity between ChatGPT hype and the words emitted by a used car salesman.

Bystander and russ_watters
Except that used car salesmen occasionally have actual cars.

aaroman, russ_watters and Philip Koeck
My question requires analytic geometry. AI (chatgpt or Bingchat) don;t have it.

I asked the AI to give my life purpose, and it didn't know how. I was so disappointed.

pinball1970
mathman said:
My question requires analytic geometry. AI (chatgpt or Bingchat) don;t have it.
If you want to be more systematic in testing their capabilities, you should try first asking them elementary questions about the constructions in your problem, and then gradually make the task more difficult.

Greg Bernhardt said:
You'll likely need to wait for the Wolfram Alpha plugin to get out of early access for more confident math results.

ChatGPT is easily confused with operators in math as a large language model.

I don't think ChatGPT can do geometry, although it can do very simple arithmetics.

If enough people put a proof on the web, ChatGPT can echo it back.

In the words of John Entwistle:

Everything I do has been done before
Someone else has said.

## 1. How do you determine the radius of the semi-circle inscribed in a triangle?

To determine the radius of the semi-circle inscribed in a triangle, you can use the formula r = A / s, where r is the radius, A is the area of the triangle, and s is the semi-perimeter of the triangle.

## 2. What is the relationship between the radius of the semi-circle and the sides of the triangle?

The radius of the semi-circle inscribed in a triangle is related to the sides of the triangle through the formula r = A / s, where r is the radius, A is the area of the triangle, and s is the semi-perimeter of the triangle.

## 3. How do you find the area of the triangle inscribed in a semi-circle?

To find the area of the triangle inscribed in a semi-circle, you can use the formula A = r * s, where A is the area of the triangle, r is the radius of the semi-circle, and s is the semi-perimeter of the triangle.

## 4. Can the semi-circle be inscribed in any type of triangle?

Yes, a semi-circle can be inscribed in any type of triangle, including equilateral, isosceles, and scalene triangles. The radius of the semi-circle will vary depending on the size and shape of the triangle.

## 5. How can the semi-circle inside triangle geometry problem be useful in real-world applications?

The semi-circle inside triangle geometry problem can be useful in various real-world applications, such as architecture, engineering, and computer graphics. Understanding the relationship between the semi-circle and the triangle can help in designing structures, calculating areas, and creating visual representations.

• Computing and Technology
Replies
21
Views
2K
• Calculus and Beyond Homework Help
Replies
6
Views
1K
• Introductory Physics Homework Help
Replies
9
Views
374
• Precalculus Mathematics Homework Help
Replies
21
Views
3K
• General Math
Replies
1
Views
7K
• Introductory Physics Homework Help
Replies
43
Views
3K
• Precalculus Mathematics Homework Help
Replies
3
Views
2K
• Precalculus Mathematics Homework Help
Replies
13
Views
2K
• Calculus
Replies
6
Views
4K
• General Math
Replies
30
Views
7K