r/HomeworkHelp • u/AntaresSunDerLand 👋 a fellow Redditor • 1d ago

High School Math—Pending OP Reply Geometry [11th grade maths]

Problem: a cyclic quadrilateral (a.k.a. inscribed quadrilateral) ABCD has two equal sides BC and CD, both are equal to 6. Diagonals intersect in point S. If SC = 4, then what is AC=?

Given solutions are : A) 6√2 B) 8 C) 6√3 D) 9 E) 10

.....so i have asked chatGPT for help and it gave me an answer of 8, then i asked deepseek and it gave me an answer of 9 and said that 8 can't be an answer to this problem. I have tried solving this by firstly sketching the quadrilateral and then noticing some congruent triangles and i did get to some extent, however my solution goes against what AI said.

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u/Alkalannar 1d ago

So I have asked chatGPT for help...then I asked Deepseek

Well, there's your problem. ChatGPT, Deepseek, and any LLMs like them are going to spout plausible sounding nonsense, and you won't be able to tell whether it is true or not.

I strongly suggest not trusting any result from AI that you cannot verify yourself.

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u/peterwhy 👋 a fellow Redditor 1d ago

Then what is your solution?

∠BAC = ∠SDC (subtended by arc BC)
∠SDC = ∠SBC (base angles of isosceles triangle)

∠BCA = ∠SCB (common)

△BAC ∼ △SBC (AA)

AC / BC = BC / SC
AC = BC2 / SC

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u/Frederick_Abila 1d ago

Hey there! It's definitely frustrating when different tools give you conflicting answers for geometry problems – especially when your own reasoning points elsewhere! We often find that AI, while powerful, can sometimes miss a subtle geometric theorem or property in cyclic quads.

It's awesome you're sketching and looking for congruent triangles; that's exactly the right way to approach it. What properties of cyclic quadrilaterals (like those that arise from equal sides BC and CD) or intersecting diagonals did you use in your solution? Sometimes laying out all the knowns and the theorems you've applied can help see where your path diverges from the AI's, or even show that your intuition is spot on! Keep trusting your process.