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"value": "Return your final response within \\boxed{}. Let $ ABC $ be an obtuse triangle with $ \\angle A > 90^{\\circ} $ . Let circle $ O $ be the circumcircle of $ ABC $ . $ D $ is a point lying on segment $ AB $ such that $ AD = AC $ . Let $ AK $ be the diameter of circle ... |
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"value": "Return your final response within \\boxed{}. Chloe wants to buy a hoodie that costs $\\$32.75$. She empties her wallet and finds she only has three $\\$10$ bills, eight quarters, and a pile of dimes. What is the minimum number of dimes that must be in her pile so she can pay for ... |
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"value": "Return your final response within \\boxed{}. Point \\( O \\) is the center of the inscribed circle in triangle \\( ABC \\). Points \\( M \\) and \\( K \\) are chosen on sides \\( AC \\) and \\( BC \\) respectively such that \\( BK \\cdot AB = BO^2 \\) and \\( AM \\cdot AB = AO^2 ... |
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"value": "Return your final response within \\boxed{}. People enter the subway uniformly from the street. After passing through the turnstiles, they end up in a small hall before the escalators. The entrance doors have just opened, and initially, the hall before the escalators was empty, w... |
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"value": "Return your final response within \\boxed{}. There are 55 numbers arranged in a circle, each of which is equal to the sum of its neighboring numbers. Prove that all the numbers are equal to zero."
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"value": "<think>\n\nOkay, let's see. I need ... |
[{"from":"user","value":"Return your final response within \\boxed{}. Let \\( f(x) = A\\left(x^{2}-2(...TRUNCATED) |
[{"from":"user","value":"What is the heat of crystallization for 100 grams of sodium acetate trihydr(...TRUNCATED) |
[{"from":"user","value":"Generate an executable Python function generated from the given prompt. The(...TRUNCATED) |
[{"from":"user","value":"Return your final response within \\boxed{}. The point of intersection of t(...TRUNCATED) |
[{"from":"user","value":"Return your final response within \\boxed{}. Given a cyclic quadrilateral \(...TRUNCATED) |
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