<｜begin▁of▁sentence｜>### Instruction:
As a forensic linguist, you may be asked to assist in a criminal investigation involving a case of cyber fraud. The investigators have obtained a set of control points for a Bezier curve [(0, 0), (1, 2), (2, 0)] that are suspected to be part of a malicious code used to alter financial transaction data. Additionally, the investigators have found evidence of a circle centered at the curve's end point with a radius of 1.0, which may correspond to a protective encryption layer.

In order to analyze the code and its potential impact, the investigators are seeking your expertise to utilize a binary search solver to find the precise coordinates where the Bezier curve intersects with the circle. This information could provide critical insights into the functionality and potential vulnerabilities of the code. As a forensic linguist, you are uniquely positioned to apply linguistic and analytical techniques to this complex technical challenge to aid in the investigation.
### Response:
import numpy as np
from scipy.optimize import bisect

def bezier(t, points):
    # A function to calculate the position on a Bezier curve given control points
    n = len(points) - 1
    return sum(comb(n, i) * (1-t)**(n-i) * t**i * np.array(points[i]) for i in range(n + 1))


def find_intersection(bezier_points, circle_center, circle_radius):
    # Find intersection of a Bezier curve and a circle using binary search

    def distance_from_circle(t):
        point_on_curve = bezier(t, bezier_points)
        return np.linalg.norm(point_on_curve - circle_center) - circle_radius
    
    t_intersection = bisect(distance_from_circle, 0, 1)
    intersection_point = bezier(t_intersection, bezier_points)
    return intersection_point.tolist()

# Example usage:
bezier_points = [(0, 0), (1, 2), (2, 0)]
circle_center = bezier_points[-1]
circle_radius = 1.0
intersection = find_intersection(bezier_points, circle_center, circle_radius)
print(intersection)
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