Well?
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ChatGPT: 2.9348637069 UnitsGrok: 0.9625 UnitsClaude: 2.318 Units
>>16929493*the hand movements*
>>16929495Gemini via Google Image Search: 0.8 Units
>>16929497Four different AI's with four different answers. Surely this will replace humans
>>16929486i give up but thanks for the template, i was looking for it for a while
>>16929502Math-GPT.org says the radius is 2 Units, and included all of this.
>>16929502Just gotta take the vibe average.I call it The Wisdom of AI Crowds.
>black triangle contains 25703 pixels>circle contains 24578 pixels>heron's formula gives 8.1815>r = sqrt[24758*8.1815/(25703*pi)]>r = 1.58
>>16929506DeepAI Math says 1.26 units. ThetaWise asked me for clarification, first one to do that, wanting me to verify which edges the circle is tangent to. Result: 1.5723590188Hey that's pretty close to >>16929510
>>16929521Almost looks like it's pi/2
>>16929486This is what simulation software was made for
>>16929486I got everything except for the circle I guess I don't know shit about how circles work.
VS Code + Copilot, GPT 5.4This one is exciting, full of twists and turns, countless python libraries.We're at 15 minutes in it's asking for an approval:>$ProgressPreference='SilentlyContinue'; Invoke-WebRequest -UseBasicParsing "https://www.google.com/search?q=\"Two+triangles+and+a+circle+are+inside+a+square\"+\"triangle+BDC+are+8,+4+and+5\"" | Select-Object -ExpandProperty Content | Out-StringIt's been another ~5 minutes, it wants another:>$ProgressPreference='SilentlyContinue'; $url = 'https://www.bing.com/search?q=Two+triangles+and+a+circle+are+inside+a+square+triangle+BDC+8+4+5'; (Invoke-WebRequest -UseBasicParsing $url).Content | Out-StringIt's been about a half hour total so far and it claims to be writing the solver.>I’m writing the solver now. It will reconstruct the key geometry directly from problem.png, annotate each detected feature, and save a step-by-step visualization plus the computed radius.>python .\solve.py .\circle.png>Saved step-by-step visualization to: .\solution_steps.png>Detected radius ≈ 1.547 units>This is reconstructed directly from the image using line, contour, and circle detection.
>>16929565Tell it to label every angle and side
>>16929486r≈3.24255, pretty straightforward, no real tricks, just long-ish
>>16929543Just look up an inradius formula for a triangle (extend the lines). The formula itself is simple to prove/understand why it's true (just look it up)
Decided to see how quick this would be in CAD, took about 1 minute with very little thought involved.The radius of the circle is 1.531 units.
>>16929486My bad, >>16929575, forgot a term somewhere, it's r≈1.47219
>>16929588what do you get for your other lengths?
>>16929592this I guess
>>16929569I tried. It has not gone well.
>>16929599Oh i see what I did wrong, yes
>>16929588Now do the closed form
>>16929638[math]256r^4-1792r^3+4016r^2-3328r+841=0[/math][math]r=\frac{1}{8}\sqrt{112-16\sqrt{33}-8\sqrt{70-12\sqrt{33}}}\approx1.531[/math]
>>16929650Looks like it's not right
>>16929653I didn't question the robot.
>>16929638Not possible, it's just a bunch of quadratic intersections, so like an at least an 8th degree polynomial. You could easily write it in terms of the top lengths though with inradius and trig
>>16929486system:5^2 + 4^2 – 2*5*4*Cos[γ] = 8^2δ + ε = π – γ(5*Cos[δ])*(5*Sin[δ])/2 = (4*Cos[ε])*(4*Sin[ε])/2s = 5*Cos[δ] + 4*Cos[ε]π/2 < γ < π0 < δ < π/20 < ε < π/2solution:Cos[γ] = –23/40Cos[δ] = Sqrt[50 + 979/Sqrt[610]]/10Cos[ε] = Sqrt[32 + 241/Sqrt[610]]/8s = Sqrt[128 + 1553*Sqrt[2/305]]/2vertices of square:O = (0, 0)A = (0, s)E = (s, s)F = (s, 0)vertices of obtuse triangle:B = (0, s – 5*Sin[δ])C = (5*Cos[δ], s)D = (s, s – 4*Sin[ε])
>>16929486the greeks wouldve figured this out with a piece of string
>>16929495Gemini: The radius of the blue circle is 1.
>>16930112That cant be 1, because from >>16929497 it's 0.8.It's silly
>>16929506>>16929521>muh aikys
>>16929565>>16930112>>16930654I forgot about these. KYS.
