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import matplotlib.pyplot as plt
import numpy as np

# Set up the figure
fig, ax = plt.subplots()

# Draw a circle
circle = plt.Circle((0, 0), 1, edgecolor='black', fill=False)
ax.add_artist(circle)

# Draw central angle
central_angle_x = [0, np.cos(np.radians(30)), np.cos(np.radians(150))]
central_angle_y = [0, np.sin(np.radians(30)), np.sin(np.radians(150))]
ax.plot(central_angle_x, central_angle_y, marker='o', color='blue', label="Central Angle")

# Draw inscribed angle B
inscribed_angle_x = [np.cos(np.radians(210)), 0, np.cos(np.radians(330))]
inscribed_angle_y = [np.sin(np.radians(210)), 1, np.sin(np.radians(330))]
ax.plot(inscribed_angle_x, inscribed_angle_y, marker='o', color='green', label="Inscribed Angle B")

# Points C and D on the circle
ax.plot(np.cos(np.radians(45)), np.sin(np.radians(45)), 'ro', label="Point C")
ax.plot(np.cos(np.radians(135)), np.sin(np.radians(135)), 'ro', label="Point D")

# Points E and F outside the circle
ax.plot(1.5, 1.5, 'bo', label="Point E")
ax.plot(-1.5, 1.5, 'bo', label="Point F")

# Intercepted arc by a central angle G
arc_G_angles = np.linspace(30, 150, 100)
arc_G_x = np.cos(np.radians(arc_G_angles))
arc_G_y = np.sin(np.radians(arc_G_angles))
ax.plot(arc_G_x, arc_G_y, color='blue', linestyle='--', label="Intercepted Arc by Central Angle G")

# Intercepted arc by an inscribed angle H
arc_H_angles = np.linspace(210, 330, 100)
arc_H_x = np.cos(np.radians(arc_H_angles))
arc_H_y = np.sin(np.radians(arc_H_angles))
ax.plot(arc_H_x, arc_H_y, color='green', linestyle='--', label="Intercepted Arc by Inscribed Angle H")

# Setting up the plot limits and aspect ratio
ax.set_aspect('equal')
ax.set_xlim(-2, 2)
ax.set_ylim(-2, 2)

# Hide axes
ax.axis('off')

# Add legend
ax.legend(loc='upper right')

# Display the plot
plt.show()