## Excursions in advanced euclidean geometryThis book is directed to readers who have a genuine desire to extend their study of Euclidean geometry beyond the high school course, and who can appreciate the beauty that lies ahead in advanced Euclidean geometry. |

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### Contents

CONCURRENCY OF LINES IN A TRIANGLE | 24 |

COLLINEARITY OF POINTS | 38 |

SOME SYMMETRIC POINTS IN A TRIANGLE | 65 |

Copyright | |

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### Common terms and phrases

ADEF altitudes APPLICATION bisect Brianchon's Theorem centroid Ceva's Theorem circumcircle of AABC collinear congruent consider construct cyclic quadrilateral diagonals Draw equicircles equilateral triangle Euclidean geometry excircle exterior fallacy Fibonacci Numbers given triangle golden ratio golden rectangle hexagon high school geometry hypotenuse incircle inscribed interior angle bisectors isosceles joining the midpoints lengths line containing ln AABC ln Figure Lucas Numbers mathematical induction measure medians meet Menelaus Menelaus'Theorem midline mLABC mLACB nine point circle opposite sides orthic triangle orthocenter pair of opposite parallel parallelogram Pascal's Theorem perpendicular bisector point of intersection PROOF properties Prove Ptolemy's Theorem Pythagorean Theorem quadrilateral ABCD radical axis relationships respectively right angle right triangle secant segments joining Similarly Simson Line Simson's Theorem square Stewart's Theorem tangent segments trapezoid triangle equals vertex vertices