PROBLEMS & SOLUTIONSINS EUCLIDEAN

M. N. AREF AND WILLIAM WERNICK

INS PROBLEMS &

SOLUTIONS EUCLIDEAN

GEOMETRY

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HANDBOOK OF MATHEMATICAL FUNCTIONS: WITH FORMULAS, GRAPHS, AND MATHEMATICAL

TABLES, Edited by Milton Abramowitz and Irene A. Stegun. (0-486-61272-4)

ABSTRACT AND CONCRETE CATEGORIES: THE JOY OF CATS, Jiri Adamek, Horst Herrlich, George E. Strecker. (0-486-46934-4)

NONSTANDARD METHODS IN STOCHASTIC ANALYSIS AND MATHEMATICAL PHYSICS, Sergio

Albeverio, Jens Erik Fenstad, Raphael Hoegh-Krohn and Tom Lindstrom. (0-486-46899-2)

MATHEMATICS: ITS CONTENT, METHODS AND MEANING, A. D. Aleksandrov, A. N. Kolmogorov, and M. A. Lavrent'ev. (0-486-40916-3)

COLLEGE GEOMETRY: AN INTRODUCTION TO THE MODERN GEOMETRY OF THE TRIANGLE AND THE

CIRCLE, Nathan Altshiller-Court. (0-486-45805-9)

THE WORKS OF ARCHIMEDES, Archimedes. Translated by Sir Thomas Heath. (0-486-42084-1)

REAL VARIABLES WITH BASIC METRIC SPACE TOPOLOGY, Robert B. Ash. (0-486-47220-5) INTRODUCTION TO DIFFERENTIABLE MANIFOLDS, Louis Auslander and Robert E. MacKenzie.

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PROBLEM SOLVING THROUGH RECREATIONAL MATHEMATICS, Bonnie Averbach and Orin Chein. (0-486-40917-1)

THEORY OF LINEAR OPERATIONS, Stefan Banach. Translated by F. Jellett. (0-486-46983-2)

VECTOR CALCULUS, Peter Baxandall and Hans Liebeck. (0-486-46620-5)

INTRODUCTION TO VECTORS AND TENSORS: SECOND EDITION-TWO VOLUMES BOUND AS ONE,

Ray M. Bowen and C: C. Wang. (0-486-46914-X) ADVANCED TRIGONOMETRY, C. V. Durell and A. Robson. (0-486-43229-7)

FOURIER ANALYSIS IN SEVERAL COMPLEX VARIABLES, Leon Ehrenpreis. (0-486-44975-0) THE THIRTEEN BOOKS OF THE ELEMENTS, VOL. 1, Euclid. Edited by Thomas L. Heath.

(0-486-60088-2) THE THIRTEEN BOOKS OF THE ELEMENTS, VOL. 2, Euclid. (0-486-60089-0) THE THIRTEEN BOOKS OF THE ELEMENTS, VOL. 3, Euclid. Edited by Thomas L. Heath.

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AN INTRODUCTION TO DIFFERENTIAL EQUATIONS AND THEIR APPLICATIONS, Stanley J. Farlow.

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PARTIAL DIFFERENTIAL EQUATIONS FOR SCIENTISTS AND ENGINEERS, Stanley J. Farlow.

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STOCHASTIC DIFFERENTIAL EQUATIONS AND APPLICATIONS, Avner Friedman. (0-486-45359-6) ADVANCED CALCULUS, Avner Friedman. (0-486-45795-8) POINT SET TOPOLOGY, Steven A. Gaal. (0-486-47222-1) DISCOVERING MATHEMATICS: THE ART OF INVESTIGATION, A. Gardiner. (0-486-45299-9) LATTICE THEORY: FIRST CONCEPTS AND DISTRIBUTIVE LATTICES, George Gratzer.

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(continued on back flap)

PROBLEMS AND SOLUTIONS

IN

EUCLIDEAN GEOMETRY

PROBLEMS AND SOLUTIONS

IN

EUCLIDEAN GEOMETRY

M. N. AREF

Alexandria University

WILLIAM WERNICK

City College, NewYork

DOVER PUBLICATIONS, INC

MINEOLA, NEW YORK

Copyright Copyright ? 1968 by Dover Publications, Inc. All rights reserved.

Bibliographical Note This Dover edition, first published in 2010, is a reissue of a work originally published by Dover Publications, Inc, in 1968.

International Standard Book Number ISBN-13: 978-0-486-47720-6 ISBN-10: 0-486-47720-7

Manufactured in the United States by Courier Corporation 47720701



Dedicated to my father who has been always of lifelong inspiration

and encouragement to me

M.N.A.

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