In an isosceles triangle ABC with AB=BC, a square CDEF is constructed with D on BC and E on AB. The side EF intersects AC at G. Prove that the length of EG equals the diameter of the incircle of triangle BDE.

Square within triangle,

Intersecting lines reveal,

Circle's hidden truth.

Vocabulary | Description |
---|---|

Isosceles Triangle | A triangle with two sides of equal length. |

Isosceles Triangle ABC | An isosceles triangle where AB = BC. |

Square CDEF | A square constructed such that vertex D lies on BC and vertex E lies on AB. |

Point G | The intersection point of side EF of the square with AC of the triangle. |

EG | The segment from E to G, which we need to prove is equal to the diameter of the incircle of triangle BDE. |

Incircle | The largest circle that fits inside a triangle, touching all three sides. |

Diameter of the Incircle | Twice the radius of the incircle, which is the circle inscribed within triangle BDE. |

Geometry Problems

Open Problems

Visual Index

All Problems

Angles

Triangle

Isosceles Triangle

Right Triangle

Circle

Incircle

Diameter

Quadrilateral

Square

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