In a circle with center O, diameters AB and CD are perpendicular. The diameter AB is extended to a point E. From a point F on the arc AD, a tangent is drawn to point G, where GE is perpendicular to AE. Line GH is perpendicular to FB. If FH measures 8 units and HB measures 2 units, find the area of triangle BCE.

Circle's single touch,

Tangent and right lines align,

Find the area's truth.

Hints, Key Term | Description |
---|---|

Circle | A set of all points in a plane that are at a given distance from a fixed point, called the center (O in this case). |

Diameter | A straight line passing from side to side through the center of a circle. In this problem, AB and CD are diameters. |

Perpendicular | Two lines or segments that intersect to form a right angle (90 degrees). In this problem, AB and CD are perpendicular diameters. |

Tangent | A line that touches a circle at exactly one point. In this problem, the tangent is drawn from point F to point G. |

Radius | A straight line from the center of a circle to any point on its circumference. This term is crucial in solving problems involving circles and tangents. |

Right Angle | An angle of 90 degrees. In this problem, GE is perpendicular to AE and GH is perpendicular to FB, forming right angles. |

Pythagorean Theorem | A mathematical principle used to find the lengths of sides in a right triangle, expressed as a^{2} + b^{2} = c^{2}, where c is the hypotenuse. |

Tangent and Radius Theorem | A theorem stating that a tangent to a circle is perpendicular to the radius drawn to the point of tangency. This theorem is used to solve problems involving tangents and radii. |

Area of Triangle | The space enclosed by three sides. In this problem, we need to find the area of triangle BCE. |

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