G.10 circle

I.def.15

A circle ( A B ) is a plane figure contained by one arc defined by a center A and a point B establishing its defining radius / A B /, such that all segments / A B /, / A C /, / A D / falling upon the arc from A are equal.
circle_radii(( A B )) → / A B / = / A C / = / A D /
A B C D

Dependency Graph

digraph { bgcolor="transparent"; node [shape=box, style="rounded,filled", fontname="Helvetica", fontsize=11, color="#d6d3cd", fontcolor="#ffffff"]; edge [color="#8c857b", fontcolor="#8c857b", arrowsize=0.75]; rankdir="TB"; "G.1" [label="G.1", tooltip="G.1 (I.def.1): A point A is that which has no part.", fillcolor="#224422", URL="../G.1/index.html", target="_top"]; "G.2" [label="G.2", tooltip="G.2 (I.def.2): A line [ A B ] is a projection of a relationship of two points A, B.", fillcolor="#224422", URL="../G.2/index.html", target="_top"]; "G.3" [label="G.3", tooltip="G.3 (I.def.3): The extremities of a segment / A B / are points A, B.", fillcolor="#224422", URL="../G.3/index.html", target="_top"]; "G.4" [label="G.4", tooltip="G.4 (I.def.4): A segment / A B / is a portion of a line [ A B ] between two points A, B on the line.", fillcolor="#224422", URL="../G.4/index.html", target="_top"]; "G.5" [label="G.5", tooltip="G.5 (I.def.5): A surface is that which has length and breadth only.", fillcolor="#224422", URL="../G.5/index.html", target="_top"]; "G.6" [label="G.6", tooltip="G.6 (I.def.6): The extremities of a surface are lines or arcs.", fillcolor="#224422", URL="../G.6/index.html", target="_top"]; "G.7" [label="G.7", tooltip="G.7 (I.def.7): A plane surface lies evenly with the lines on itself.", fillcolor="#224422", URL="../G.7/index.html", target="_top"]; "G.8" [label="G.8", tooltip="G.8 (I.def.13): A boundary is the extremity of anything.", fillcolor="#224422", URL="../G.8/index.html", target="_top"]; "G.9" [label="G.9", tooltip="G.9 (I.def.14): A figure is that which is contained by any boundary or boundaries.", fillcolor="#224422", URL="../G.9/index.html", target="_top"]; "G.10" [label="G.10", tooltip="G.10 (I.def.15): A circle ( A B ) is a plane figure contained by one arc defined by a center A and a point B establishing its defining radius / A B /, such that all segments / A B /, / A C /, / A D...", penwidth=2.5, color="#e8b85a", fillcolor="#4a453b", URL="index.html", target="_top"]; "G.2" -> "G.1"; "G.3" -> "G.1"; "G.4" -> "G.1"; "G.10" -> "G.1"; "G.3" -> "G.2"; "G.4" -> "G.2"; "G.6" -> "G.2"; "G.7" -> "G.2"; "G.4" -> "G.3"; "G.6" -> "G.3"; "G.8" -> "G.3"; "G.7" -> "G.4"; "G.10" -> "G.4"; "G.6" -> "G.5"; "G.7" -> "G.5"; "G.10" -> "G.6"; "G.10" -> "G.7"; "G.9" -> "G.8"; "G.10" -> "G.9"; }

Required for

G.11, G.15, G.17, G.20, G.21, G.25, G.27, G.28, G.29, G.31, G.32, G.34, G.35, G.37, G.39, G.40, G.41, G.42, G.43, G.44, G.45, G.46, G.47, G.48, G.49, G.50, G.51, G.53, G.54, G.56, G.57, G.58, G.59, G.60, G.61, G.62, G.64, G.65, G.66, G.67, G.68, G.69, G.70, G.71, G.72, G.73, G.74, G.75, G.79, G.80, G.82, G.83, G.84, G.85, G.86, G.87, G.88, G.89, G.90, G.91, G.92, G.93, G.94, G.95, G.96, G.97, G.98, G.99, G.100, G.101, G.102, G.104, G.105, G.106, G.107, G.108, G.109, G.110, G.111, G.112, G.113, G.114, G.116, G.117, G.118, G.119, G.120, G.121, G.122, G.123, G.124, G.125, G.126, G.128, G.129, G.130, G.131, G.133, G.134, G.135, G.136, G.137, G.139, G.140, G.141, G.142, G.143, G.144, G.145, G.146, G.147, G.148, G.149, G.150, G.151, G.153, G.154, G.156, G.157, G.158, G.159, G.160, G.161, G.162, G.163, G.164, G.165, G.166, G.167, G.168, G.210, G.211, G.212, G.213, G.214, G.215, G.216, G.218, G.219, G.220, G.221, G.222, G.223, G.225, G.226, G.227, G.228, G.229, G.231, G.232, G.234, G.235, G.236, G.237, G.238, G.239, G.240, G.241, G.243, G.244, G.245, G.246, G.345, G.377, G.378, G.381, G.382, G.383, G.384, G.385, G.386, G.389, G.390, G.393, G.394, G.395, G.396, G.397, G.398, G.399, G.400, G.401, G.402, G.403, G.404, G.405, G.406, G.407, G.408, G.409, G.410, G.411, G.412, G.413, G.414, G.415, G.416, G.417, G.418, G.419, G.420, G.421, G.423, G.425, G.427, G.429, G.431, G.433, G.434, G.435, G.436, G.437, G.438, G.439, G.440, G.441, G.442, G.443, G.444, G.445, G.446, G.447, G.448, G.449, G.450, G.451, G.452, G.453, G.455, G.457, G.458, G.459, G.460, G.461, G.462, G.463, G.464, G.465, G.466, G.467, G.468, G.470, G.472, G.474, G.476, G.477, G.478, G.479, G.480, G.481, G.482, G.483, G.484, G.485, G.486, G.487, G.488, G.489, G.490, G.491, G.492, G.493, G.494, G.495, G.496, G.497, G.498, G.499, G.500, G.501, G.502, G.503, G.506, G.507, G.508, G.510, G.511, G.512, G.513, G.514, G.517, G.518, G.519, G.520, G.522, G.525, G.526, G.527, G.528, G.530, G.531, G.532, G.536, G.538, G.539, G.540, G.541, G.542, G.543, G.544, G.545, G.546, G.547, G.549, G.550, G.551, G.552, G.554, G.555, G.556, G.557, G.558, G.559, G.560, G.563, G.565, G.566, G.568, G.569, G.570, G.571, G.572, G.573, G.574, G.575, G.576, G.577, G.578, G.579, G.580, G.581, G.582, G.583, G.584, G.585, G.586, G.587, G.588, G.589, G.590, G.591, G.592, G.594, G.595, G.597, G.598, G.600, G.601