{"status": "success", "data": {"description_md": "Rectangle $ABCD$ has sides $\\overline {AB}$ of length 4 and $\\overline {CB}$ of length 3. Divide $\\overline {AB}$ into 168 congruent segments with points $A=P_0, P_1, \\ldots, P_{168}=B$, and divide $\\overline {CB}$ into 168 congruent segments with points $C=Q_0, Q_1, \\ldots, Q_{168}=B$. For $1 \\le k \\le 167$, draw the segments $\\overline {P_kQ_k}$. Repeat this construction on the sides $\\overline {AD}$ and $\\overline {CD}$, and then draw the diagonal $\\overline {AC}$. Find the sum of the lengths of the 335 parallel segments drawn.\n___\nLeading zeroes must be inputted, so if your answer is `34`, then input `034`. Full credit goes to [MAA](https://maa.org/) for authoring these problems. These problems were taken on the [AOPS](https://artofproblemsolving.com/) website.", "description_html": "<p>Rectangle <span class=\"katex--inline\">ABCD</span> has sides <span class=\"katex--inline\">\\overline {AB}</span> of length 4 and <span class=\"katex--inline\">\\overline {CB}</span> of length 3. Divide <span class=\"katex--inline\">\\overline {AB}</span> into 168 congruent segments with points <span class=\"katex--inline\">A=P_0, P_1, \\ldots, P_{168}=B</span>, and divide <span class=\"katex--inline\">\\overline {CB}</span> into 168 congruent segments with points <span class=\"katex--inline\">C=Q_0, Q_1, \\ldots, Q_{168}=B</span>. For <span class=\"katex--inline\">1 \\le k \\le 167</span>, draw the segments <span class=\"katex--inline\">\\overline {P_kQ_k}</span>. Repeat this construction on the sides <span class=\"katex--inline\">\\overline {AD}</span> and <span class=\"katex--inline\">\\overline {CD}</span>, and then draw the diagonal <span class=\"katex--inline\">\\overline {AC}</span>. Find the sum of the lengths of the 335 parallel segments drawn.</p>&#10;<hr><p>Leading zeroes must be inputted, so if your answer is <code>34</code>, then input <code>034</code>. Full credit goes to <a href=\"https://maa.org/\">MAA</a> for authoring these problems. These problems were taken on the <a href=\"https://artofproblemsolving.com/\">AOPS</a> website.</p>", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 3, "problem_name": "1991 AIME Problem 2", "can_next": true, "can_prev": true, "nxt": "/problem/91_aime_p03", "prev": "/problem/91_aime_p01"}}