{"id":442,"date":"2025-07-07T17:46:59","date_gmt":"2025-07-07T08:46:59","guid":{"rendered":"https:\/\/math-friend.com\/?p=442"},"modified":"2025-08-01T09:30:51","modified_gmt":"2025-08-01T00:30:51","slug":"%e3%80%90%e4%b9%9d%e5%b7%9e%e5%a4%a7%e5%ad%a6%e5%85%a5%e8%a9%a6%e3%80%91%e5%86%86%e5%91%a8%e4%b8%8a%e3%81%ae%e7%82%b9%e3%82%92%e7%b5%90%e3%82%93%e3%81%a7%e3%81%a7%e3%81%8d%e3%82%8b%e4%b8%89%e8%a7%92","status":"publish","type":"post","link":"https:\/\/math-friend.com\/?p=442","title":{"rendered":"\u3010\u4e5d\u5dde\u5927\u5b66\u5165\u8a66\u3011\u5186\u5468\u4e0a\u306e\u70b9\u3092\u7d50\u3093\u3067\u3067\u304d\u308b\u4e09\u89d2\u5f62\u306e\u9762\u7a4d(2025)"},"content":{"rendered":"\n

\u4eca\u56de\u306f\u3053\u3061\u3089\u306e\u554f\u984c\u3092\u89e3\u3044\u3066\u3044\u304d\u307e\u3059.<\/p>\n\n\n\n

\u70b9O\u3092\u4e2d\u5fc3\u3068\u3059\u308b\u534a\u5f84\\(1\\)\u306e\u5186\u5468\u4e0a\u306b, \u4ee5\u4e0b\u306e3\u6761\u4ef6\u3092\u6e80\u305f\u3059\u3088\u3046\u306b4\u70b9A, B, C, D\u3092\u3068\u308b.

\u30fb\u70b9A, B, C, D\u306f\u5186\u5468\u4e0a\u3067\u53cd\u6642\u8a08\u56de\u308a\u306b\u3053\u306e\u9806\u3067\u4e26\u3076
\u30fb\u7dda\u5206\\(AD\\)\u306f\u5186\u306e\u76f4\u5f84
\u30fb\\(AC=CD\\)
\u30fb\\(AB=BC\\)

\u307e\u305f, \u7dda\u5206\\(AC\\)\u3068\u7dda\u5206\\(BD\\)\u306e\u4ea4\u70b9\u3092E\u3068\u3059\u308b. \u3053\u306e\u3068\u304d, \u4ee5\u4e0b\u306e\u5024\u3092\u305d\u308c\u305e\u308c\u6c42\u3081\u3088.
(1) \\(\\angle{ACB}\\)
(2) \\(BC\\)
(3) \u4e09\u89d2\u5f62\\(BCE\\)\u306e\u9762\u7a4d
(2025 \u4e5d\u5dde\u5927\u5b66\u7406\u7cfb[4])<\/span><\/p>\n\n\n\n

\u3053\u3061\u3089\u554f\u984c\u6587\u306b\u56f3\u304c\u4e0e\u3048\u3089\u308c\u3066\u3044\u306a\u3044\u56f3\u5f62\u554f\u984c\u3067\u3059. \u6761\u4ef6\u304b\u3089\u9069\u5207\u306a\u56f3\u3092\u66f8\u304d\u307e\u3057\u3087\u3046. \u89e3\u7b54\u5f8c\u306b\u88dc\u8db3\u8aac\u660e\u3092\u3057\u307e\u3059\u304c, \u56f3\u306f\u305d\u308c\u306a\u308a\u306b\u7dba\u9e97\u306b\u66f8\u304f\u3079\u304d\u3067\u3059. \u56f3\u3092\u66f8\u3044\u305f\u3089\u8fba\u306e\u9577\u3055, \u89d2\u306e\u5927\u304d\u3055, \u3069\u306e\u8fba\u3068\u3069\u306e\u8fba\u306e\u5927\u304d\u3055\u304c\u7b49\u3057\u3044\u304b, \u3069\u306e\u89d2\u3068\u3069\u306e\u89d2\u304c\u7b49\u3057\u3044\u304b, \u3068\u306b\u304b\u304f\u66f8\u304d\u307e\u304f\u308a\u307e\u3057\u3087\u3046. \u305d\u3046\u3059\u308b\u3068\u9583\u304f\u3053\u3068\u3082\u3042\u308b\u306f\u305a\u3067\u3059.

\u305d\u308c\u3067\u306f\u89e3\u3044\u3066\u3044\u304d\u307e\u3057\u3087\u3046.<\/p>\n\n\n\n

\n

(1) \u4e0e\u3048\u3089\u308c\u305f\u6761\u4ef6\u304b\u3089\u56f3\u3092\u63cf\u304f\u3068\u4ee5\u4e0b\u3068\u306a\u308b.<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

\u4e09\u89d2\u5f62\\(ABC\\)\u306f\\(AB=BC\\)\u306e\u4e8c\u7b49\u8fba\u4e09\u89d2\u5f62\u306a\u306e\u3067, \u305d\u306e\u5e95\u89d2\u306f\u7b49\u3057\u304f\\(\\angle{BAC}=\\angle{BCA}\\)\u3067\u3042\u308b. \u5186\u5468\u89d2\u306e\u5b9a\u7406\u304b\u3089\\(\\angle{BAC}=\\angle{BDC}\\), \\(\\angle{BCA}=\\angle{ADB}\\)\u3068\u306a\u308b\u306e\u3067, 4\u3064\u306e\u89d2\\(\\angle{BAC}\\), \\(\\angle{BCA}\\), \\(\\angle{ADB}\\), \\(\\angle{BDC}\\)\u306f\u3044\u305a\u308c\u3082\u7b49\u3057\u3044.

\u307e\u305f, AD\u306f\u5186\u306e\u76f4\u5f84\u3067\u3042\u308b\u304b\u3089, \\(\\angle{ACD}=\\frac{\\pi}{2}\\)\u3067\u3042\u308a, \\(AC=CD\\)\u3067\u3042\u308b\u304b\u3089\u4e09\u89d2\u5f62\\(ACD\\)\u306f\\(\\angle{ACD}\\)\u304c\u76f4\u89d2\u3068\u306a\u308b\u76f4\u89d2\u4e8c\u7b49\u8fba\u4e09\u89d2\u5f62\u3067\u3042\u308b. \u3088\u3063\u3066\\(\\angle{ADC}=\\frac{\\pi}{4}\\)\u3067\u3042\u308b.

\u3053\u3053\u3067, \\(\\frac{\\pi}{4}=\\angle{ADC}=\\angle{ADB}+\\angle{BDC}=2\\angle{BCA}\\)\u3067\u3042\u308b\u304b\u3089, \\(\\angle{BCA}=\\frac{\\pi}{8}\\)\u304c\u308f\u304b\u308b.<\/p>\n\n\n\n

(2) \u4e09\u89d2\u5f62\\(ABC\\)\u306f\\(AB=BC\\)\u306e\u4e8c\u7b49\u8fba\u4e09\u89d2\u5f62\u3067\u3042\u308a, (1)\u304b\u3089\\(\\angle{BAC}=\\angle{BCA}=\\frac{\\pi}{8}\\)\u3067\u3042\u308b\u304b\u3089,
$$
\\angle{ABC}=\\pi-\\angle{BAC}-\\angle{BCA}=\\frac{3\\pi}{4}
$$\u3067\u3042\u308b. \u307e\u305f, \u4e09\u89d2\u5f62\\(ACD\\)\u306f\\(AC=CD\\), \\(AD=2\\)\u3068\u306a\u308b\u76f4\u89d2\u4e8c\u7b49\u8fba\u4e09\u89d2\u5f62\u3067\u3042\u308b\u304b\u3089, \u4e09\u5e73\u65b9\u306e\u5b9a\u7406\u304b\u3089
$$
2^2={AD}^2={AC}^2+{CD}^2=2{AC}^2
$$
\u3067\u3042\u308b\u304b\u3089, \\(AC=\\sqrt{2}\\)\u3067\u3042\u308b. \u3088\u3063\u3066, \u4e09\u89d2\u5f62\\(ABC\\)\u3067\u4f59\u5f26\u5b9a\u7406\u304b\u3089,
$$
\\begin{align}
{AC}^2&={AB}^2+{BC}^2-2{AB}\\cdot {BC}\\cos{\\angle{ABC}}\\\\[1.5ex]
\\sqrt{2}^2&=2{BC}^2-2{BC}^2\\cdot\\left(-\\frac{1}{\\sqrt{2}}\\right)\\\\[1.5ex]
{BC}^2&=\\frac{2}{2+\\sqrt{2}}\\\\[1.5ex]
{BC}&=\\sqrt{\\frac{2}{2+\\sqrt{2}}}=\\frac{\\sqrt{2}}{\\sqrt{2+\\sqrt{2}}}=\\frac{\\sqrt{2}\\sqrt{2-\\sqrt{2}}}{\\sqrt{2+\\sqrt{2}}\\sqrt{2-\\sqrt{2}}}\\\\[1.5ex]
&=\\frac{\\sqrt{2}\\sqrt{2-\\sqrt{2}}}{\\sqrt{2^2-\\sqrt{2}^2}}=\\frac{\\sqrt{2}\\sqrt{2-\\sqrt{2}}}{\\sqrt{2}}=\\sqrt{2-\\sqrt{2}}
\\end{align}
$$
\u3068\u306a\u308a, \\(BC\\)\u304c\u6c42\u307e\u3063\u305f.<\/p>\n\n\n\n

(3) \u4e09\u89d2\u5f62\\(ADC\\)\u306b\u304a\u3044\u3066\\(\\angle{ADE}=\\angle{CDE}\\)\u3088\u308a, \\(DE\\)\u306f\\(\\angle{ADC}\\)\u306e\u4e8c\u7b49\u5206\u7dda\u3067\u3042\u308b. \u307e\u305f, \\(AD=2\\), \\(CD=AC=\\sqrt{2}\\)\u3067\u3042\u308b\u304b\u3089, \u4e09\u89d2\u5f62\u306e\u5185\u89d2\u306e\u4e8c\u7b49\u5206\u7dda\u306e\u516c\u5f0f\u3088\u308a, \\(AE:EC=AD:CD=2:\\sqrt{2}\\)\u3067\u3042\u308b. \\(AE+EC=AC=\\sqrt{2}\\)\u306b\u6ce8\u610f\u3057\u3066,
$$
\\triangle{BCE}=\\triangle{ABC}\\times\\frac{EC}{AC}=\\triangle{ABC}\\times\\frac{\\sqrt{2}}{2+\\sqrt{2}}
$$\u3067\u3042\u308b.

\u3053\u3053\u3067,
$$
\\begin{align}
\\triangle{ABC}&=\\frac{1}{2}AB\\cdot BC\\sin{\\angle{ABC}}=\\frac{1}{2}\\cdot\\sqrt{2-\\sqrt{2}}^2\\times\\frac{1}{\\sqrt{2}}\\\\[1.5ex]
&=\\frac{2-\\sqrt{2}}{2\\sqrt{2}}
\\end{align}
$$
\u3067\u3042\u308b\u304b\u3089,
$$
\\begin{align}
\\triangle{BCE}&=\\frac{2-\\sqrt{2}}{2\\sqrt{2}}\\times\\frac{\\sqrt{2}}{2+\\sqrt{2}}=\\frac{2-\\sqrt{2}}{2(2+\\sqrt{2})}\\\\[1.5ex]
&=\\frac{(2-\\sqrt{2})^2}{2(2+\\sqrt{2})(2-\\sqrt{2})}=\\frac{2(\\sqrt{2}-1)^2}{2^2}\\\\[1.5ex]
&=\\frac{3-2\\sqrt{2}}{2}
\\end{align}
$$\u3068\u306a\u308b.<\/p>\n<\/div><\/div>\n\n\n\n

\u3053\u3046\u3044\u3063\u305f\u56f3\u5f62\u554f\u984c\u306f\u89e3\u7b54\u3092\u898b\u308b\u3068\u7c21\u5358\u306b\u601d\u3048\u308b\u306e\u3067\u3059\u304c, \u81ea\u5206\u3067\u5c0e\u51fa\u3059\u308b\u306e\u306f\u306a\u304b\u306a\u304b\u96e3\u3057\u3044\u3067\u3059. \u79c1\u306f\u6700\u521d\u306b\u89e3\u3044\u305f\u3068\u304d, (1)\u3067\u4f59\u5f26\u5b9a\u7406\u3092\u7528\u3044\u3066\\(\\cos{\\angle{BCA}}\\)\u3092\u5c0e\u51fa\u3057\u305f\u306e\u3067\u3059\u304c, \u305d\u306e\u5024\u304c\u898b\u305f\u3053\u3068\u306e\u306a\u3044\u5024\u306b\u306a\u3063\u305f\u306e\u3067, \\(\\cos\\)\u306e\u5024\u304b\u3089\\(\\angle{BCA}\\)\u3092\u6c42\u3081\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u305b\u3093\u3067\u3057\u305f. \u6700\u521d\u306b\u56f3\u3092\u305d\u308c\u306a\u308a\u306b\u7dba\u9e97\u306b\u66f8\u3051\u3070, \\(\\angle{BCA}\\)\u304c\\({30}^{\\circ}\\)\u3088\u308a\u5c0f\u3055\u305d\u3046\u3068\u306f\u308f\u304b\u308a, \\({30}^{\\circ}\\)\u3088\u308a\u5c0f\u3055\u3044\u89d2\u306e\\(\\cos\\)\u306f\u666e\u901a\u899a\u3048\u3066\u3044\u306a\u3044\u3068\u3044\u3046\u3053\u3068\u304b\u3089, \u4f59\u5f26\u5b9a\u7406\u304b\u3089\u6c42\u3081\u308b\u3053\u3068\u306f\u96e3\u3057\u305d\u3046\u3067\u3042\u308b\u3068\u6c17\u3065\u304f\u3079\u304d\u3067\u3057\u305f.

\u307e\u305f, \u4eca\u56de\u306e\u554f\u984c\u3067\u306f\u4e09\u89d2\u5f62\\(ADC\\)\u306b\u304a\u3044\u3066, \\(AE\\)\u304c\\(\\angle{ADC}\\)\u306e\u4e8c\u7b49\u5206\u7dda\u306b\u306a\u3063\u3066\u3044\u308b\u3053\u3068\u306b\u6c17\u3065\u304d, \u4e8c\u7b49\u5206\u7dda\u306e\u516c\u5f0f\u3092\u4f7f\u7528\u3067\u304d\u308b\u304b\u3069\u3046\u304b\u304c\u30df\u30bd\u306b\u306a\u3063\u3066\u3044\u308b\u304b\u3068\u601d\u3044\u307e\u3059. \u53d7\u9a13\u306e\u7dca\u8feb\u3057\u305f\u72b6\u6cc1\u306e\u4e2d\u3067\u81ea\u5206\u304c\u601d\u3044\u3064\u304f\u304b\u4e0d\u5b89\u306b\u306a\u308a\u307e\u3057\u305f.

youtube\u3067\u3082\u89e3\u8aac\u3057\u3066\u3044\u307e\u3059.<\/p>\n\n\n\n