In a triangle ABC, the incircle centered at D intersects a circle tangent to the sides of angle C at points F and G. The line FG intersects side BC at H and the extension of line AD at J. Prove that points B, D, H, and J are concyclic.

Circles intersect,

Points align in perfect form,

Proof awaits us now.

Term | Description |
---|---|

Triangle ABC | A polygon with three sides and three angles. |

Incircle | A circle inscribed in a triangle, touching all three sides. |

Center D | The center point of the incircle. |

Tangent circle | A circle that touches another circle at exactly one point. |

Points F and G | Intersection points of the incircle and the tangent circle. |

Line FG | The line segment connecting points F and G. |

Point H | Intersection point of line FG and side BC. |

Line AD | The line segment connecting points A and D. |

Point J | Intersection point of line FG and the extension of line AD. |

Concyclic points | Points that lie on the same circle. |

Geometry Problems

Open Problems

Visual Index

All Problems

Angles

Triangle

Triangle Center

Incenter

Circle Tangent Line

Intersecting Circles

Quadrilateral

Concyclic
Points

Cyclic Quadrilateral

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