From 93091a373593b464ed0452215c067cb4b513157b Mon Sep 17 00:00:00 2001
From: wangweiye7840 <kj_wangweiye@126.com>
Date: Mon, 4 Mar 2024 14:22:07 +0800
Subject: [PATCH] =?UTF-8?q?=E6=B7=BB=E5=8A=A0=E4=B8=A4=E9=81=93=E5=85=B3?=
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---
 题库0.3/Problems.json | 58 +++++++++++++++++++++++++++++++++++++++++--
 1 file changed, 56 insertions(+), 2 deletions(-)

diff --git a/题库0.3/Problems.json b/题库0.3/Problems.json
index 1b2aefec..7473fdf4 100644
--- a/题库0.3/Problems.json
+++ b/题库0.3/Problems.json
@@ -46542,7 +46542,9 @@
             "20220625\t王伟叶"
         ],
         "same": [],
-        "related": [],
+        "related": [
+            "024616"
+        ],
         "remark": "",
         "space": "4em",
         "unrelated": []
@@ -49625,7 +49627,8 @@
         ],
         "same": [],
         "related": [
-            "001482"
+            "001482",
+            "024617"
         ],
         "remark": "",
         "space": "",
@@ -680632,6 +680635,57 @@
         "space": "",
         "unrelated": []
     },
+    "024616": {
+        "id": "024616",
+        "content": "在三角形$ABC$中, 记$p=\\dfrac{a+b+c}{2}$, $S$表示三角形的面积. 利用$\\sin^2A+\\cos^2A=1$, 证明:\n$$S=\\sqrt{p(p-a)(p-b)(p-c)}.$$",
+        "objs": [],
+        "tags": [
+            "第三单元"
+        ],
+        "genre": "4em",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2016届创新班作业\t2101-正弦定理与余弦定理-20240304修改",
+        "edit": [
+            "20220625\t王伟叶",
+            "20240304\t王伟叶"
+        ],
+        "same": [],
+        "related": [
+            "001370"
+        ],
+        "remark": "",
+        "space": "4em",
+        "unrelated": []
+    },
+    "024617": {
+        "id": "024617",
+        "content": "在$\\triangle ABC$中, 若$a\\cos A=b\\cos B$, 判断该三角形的形状.",
+        "objs": [],
+        "tags": [
+            "第三单元"
+        ],
+        "genre": "4em",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2016届创新班作业\t2116-判断三角形的形状-20240304修改",
+        "edit": [
+            "20220625\t王伟叶",
+            "20240304\t王伟叶"
+        ],
+        "same": [],
+        "related": [
+            "001482",
+            "001483"
+        ],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
     "030001": {
         "id": "030001",
         "content": "若$x,y,z$都是实数, 则:(填写``\\textcircled{1} 充分非必要、\\textcircled{2} 必要非充分、\\textcircled{3} 充要、\\textcircled{4} 既非充分又非必要''之一)\\\\\n(1) ``$xy=0$''是``$x=0$''的\\blank{50}条件;\\\\\n(2) ``$x\\cdot y=y\\cdot z$''是``$x=z$''的\\blank{50}条件;\\\\\n(3) ``$\\dfrac xy=\\dfrac yz$''是``$xz=y^2$''的\\blank{50}条件;\\\\\n(4) ``$|x |>| y|$''是``$x>y>0$''的\\blank{50}条件;\\\\\n(5) ``$x^2>4$''是``$x>2$'' 的\\blank{50}条件;\\\\\n(6) ``$x=-3$''是``$x^2+x-6=0$'' 的\\blank{50}条件;\\\\\n(7) ``$|x+y|<2$''是``$|x|<1$且$|y|<1$'' 的\\blank{50}条件;\\\\\n(8) ``$|x|<3$''是``$x^2<9$'' 的\\blank{50}条件;\\\\\n(9) ``$x^2+y^2>0$''是``$x\\ne 0$'' 的\\blank{50}条件;\\\\\n(10) ``$\\dfrac{x^2+x+1}{3x+2}<0$''是``$3x+2<0$'' 的\\blank{50}条件;\\\\\n(11) ``$0<x<3$''是``$|x-1|<2$'' 的\\blank{50}条件.",