From cf3ffb4a4645a78e56246ba5dc2c27dad1103a95 Mon Sep 17 00:00:00 2001
From: Maxim Dolgolyov <maxim.dolgolyov@gmail.com>
Date: Thu, 28 May 2026 19:28:06 +0300
Subject: [PATCH] =?UTF-8?q?fix(geom8=20ch4):=20=C2=A78.1=20=E2=80=94=20?=
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Маркер центрального угла α был нарисован дугой M 142,81 A 22,22 0 0,1 142,119
— стартовая точка (142,81) находилась в направлении -40° от O (между
OA и горизонталью), что НЕ совпадало с направлением радиуса OA (-60°).
Дуга выглядела не между радиусами а сбоку.

Исправлено: dуга теперь от (131,81) до (131,119) — точки лежат на
радиусах OA и OC на расстоянии 22 от центра (угол -60° и +60°
соответственно). Подпись α тоже подвинута чуть левее.

Co-Authored-By: Claude Opus 4.7 (1M context) <noreply@anthropic.com>
---
 frontend/textbooks/geometry_8_ch4.html | 8 +++++---
 1 file changed, 5 insertions(+), 3 deletions(-)

diff --git a/frontend/textbooks/geometry_8_ch4.html b/frontend/textbooks/geometry_8_ch4.html
index c77e3ae..aa9b825 100644
--- a/frontend/textbooks/geometry_8_ch4.html
+++ b/frontend/textbooks/geometry_8_ch4.html
@@ -3261,8 +3261,10 @@ function buildP8(){
         <!-- Radii OA and OC -->
         <line x1="120" y1="100" x2="155" y2="39" stroke="#0891b2" stroke-width="2"/>
         <line x1="120" y1="100" x2="155" y2="161" stroke="#0891b2" stroke-width="2"/>
-        <!-- Angle marker α at center O (arc of radius 22, between OA and OC) -->
-        <path d="M 142,81 A 22,22 0 0,1 142,119" fill="none" stroke="#f59e0b" stroke-width="2.2"/>
+        <!-- Angle marker α at center O (arc of radius 22, between OA and OC).
+             OA direction: (155-120, 39-100)/70=(0.5,-0.871), so start at O+22·(0.5,-0.871)=(131, 80.8).
+             OC direction: (155-120, 161-100)/70=(0.5, 0.871), so end at O+22·(0.5, 0.871)=(131, 119.2). -->
+        <path d="M 131,81 A 22,22 0 0,1 131,119" fill="none" stroke="#f59e0b" stroke-width="2.4"/>
         <!-- Center dot and vertex dots -->
         <circle cx="120" cy="100" r="3.5" fill="#0e7490"/>
         <circle cx="155" cy="39" r="4" fill="#0284c7"/>
@@ -3271,7 +3273,7 @@ function buildP8(){
         <text x="103" y="105" font-size="13" font-weight="800" fill="#0e7490" font-family="Unbounded,sans-serif">O</text>
         <text x="160" y="34" font-size="13" font-weight="800" fill="#0284c7" font-family="Unbounded,sans-serif">A</text>
         <text x="160" y="174" font-size="13" font-weight="800" fill="#0284c7" font-family="Unbounded,sans-serif">C</text>
-        <text x="148" y="105" font-size="13" font-weight="800" fill="#b45309" font-family="JetBrains Mono,monospace">α</text>
+        <text x="138" y="105" font-size="13" font-weight="800" fill="#b45309" font-family="JetBrains Mono,monospace">α</text>
         <text x="200" y="100" font-size="12" font-weight="800" fill="#dc2626" font-family="JetBrains Mono,monospace">⌣AC = α°</text>
         <text x="20" y="22" font-size="10" font-weight="700" fill="#0891b2">центральный угол ∠AOC</text>
       </svg>