This is the last Geometry POW of the 1997-98 school year. We will be posting the year-end totals during the first week of June.Back to the good stuff. This is your lucky day - I found this in a math puzzle book I have, and it's a little harder than the recent problems. You've got a circle and two tangents to the circle - AB and CB, with A and C being the points on the circle and B being the point where the two tangents intersect. AB = BC = 16 cm.
D is any point on the minor arc AC, and a tangent to the circle is drawn at D. This tangent intersects AB at point E and CB at point F. What is the perimeter of triangle EFB? Make sure you can convince me that you're right!
Annie says: Solutions
Comments will follow when I get back from a vacation :-)
A list of all the people who got this problem right follows the highlighted solutions below, and most of the solutions are also available.
From: Caleb Ho rdbaerg@compuserve.com Grade: 11 School: Monterey Bay Academy, Watsonville, California Subject: Geometry Problem of the week May 25-29 My solution is attached as a Word 7.0 file Name: Caleb Ho E-mail: calebho@hotmail.com Grade: 11 School: Monterey Bay Academy, CAFirst I will prove that AE = DE and CF = FD GD = GA = radius GDE = GAE = 90 (As FE and EA are both tangent to the circle) Therefore, triangle GDE is congruent to triangle GAE (RHS) AE = DE (Corresponding sides of congruent triangles) By using the same method, we can prove that CF = DF Actually, the distances from the intersection point of two tangents (Point E) to each of the points where the tangents meet the circle (Points D and A) are always equal. Then I will find the perimeter of triangle EFB As CF = DF, FB + FD = CB = 16 cm As AE = DE, DE + EB = AE = 16 cm Finally, we can know that the perimeter is FB+FD+DE+EB = 32 cm
The following students submitted correct solutions this week:
C. J. B., Grade 10, SI
Siddharth Padmanaban, Grade , Our Lady of Perpetual Succor High School, Chembur, Mumbai, India
Jon Gantman, Grade 10, Akiba Hebrew Academy, Merion, Pennsylvania
Kandace Gollomp, Grade 10, Akiba Hebrew Academy, Merion, Pennsylvania
Mike, Grade 11, Wood High School, Vacaville, California
Aurelian Voicu, Grade 12, Glenforest Secondary School, Canada
Arnold Moore, Grade , Western High School, Broward, Florida
Jeremy Jenkins, Grade 9, Casady School, Oklahoma City, Oklahoma
Jacob Ornelas, Grade , Smoky Hill High School, Aurora, Colorado
Andrew Cooledge, Grade 7, Odle Middle School, Bellevue, Washington
Anne Hines and Lauren Rossi, Grade 10, Germantown Academy, Fort Washington, Pennsylvania
Tiffanie Lam, Grade 8, Sequoia Middle School, Pleasant Hill, California
John Allen, Grade 8, Louis Pasteur Middle School, Orangevale, California
Dennis Sauers, Grade 9, St. John Bosco High School, Bellflower, California
Doug Eglen, Grade ,
Jim Nguyen, Grade 9, Smoky Hill High School, Aurora, Colorado
K. Karthikeyan, Grade 10, S. S. S. Sec-9, Bhilai, India
Beth Bowman and Crystal Cannaday and Andrew Krawczel, Grade 9, Franklin County High School, Rocky Mount, Virginia
Katie Anthony, Grade 9, Casady School, Oklahoma City, Oklahoma
Rebecca Miller-Webster, Grade 10, Oak Park and River Forest High School, Oak Park, Illinois
Helen Monisera, Grade ,
Robin Thornburg and Sherrelle Hudson, Grade 11, Shelby County High School, Columbiana, Alabama
Lauren Zucker, Grade 9, Germantown Academy, Fort Washington, Pennsylvania
Adrian Lai, Grade , Salesian School, Hong Kong
Nathan Reynolds, Grade 9, Franklin County High School, Rocky Mount, Virginia
Melissa Hackel, Grade , Granada High School, Livermore, California
Gordon Bockus Jr., Grade Freshman, Eastern Oklahoma State College, Wilburton, Oklahoma
Katy Crumpton, Grade 10, Shelby County High School, Columbiana, Alabama
Aaron Mertz, Grade 8, Plum Grove Junior High School, Rolling Meadows, Illinois
Patrick Draper, Grade 9, Normal Community West High School, Normal, Illinois
Catalina Anghel, Grade , Mackenzie High School, Deep River, Ontario, Canada
Betsy Feldman, Grade 9, Marple Newtown Senior High School, Newtown Square, Pennsylvania
David Grant, Grade , Livermore High School, Livermore, California
Houman Ebrahimi, Grade 12, Carlingford High School, Carlingford, New South Wales, Australia
Sorin Ionescu, Grade 8, Ecole Secondaire Dorval, Dorval, Quebec, Canada
Lim Yin, Grade 10, Raffles Institution, Singapore
Jonathan Emmons, Grade 9, Franklin County High School, Rocky Mount, Virginia
Brandi Marsh, Grade 9, Ethel Walker School, Simsbury, Connecticut
Andrea Medini, Grade , A. Righi, Italy
Noam Abrams, Grade 10, Akiba Hebrew Academy, Merion, Pennsylvania
Sari Yehuda, Grade 10, Akiba Hebrew Academy, Merion, Pennsylvania
Avrum Tilman, Grade 10, Akiba Hebrew Academy, Merion, Pennsylvania
Frannie Laks, Grade 10, Akiba Hebrew Academy, Merion, Pennsylvania
Hannah Margoles, Grade 10, Akiba Hebrew Academy, Merion, Pennsylvania
aaa, Grade ,
Josh Boyette, Grade 10, Akiba Hebrew Academy, Merion, Pennsylvania
Megan Via, Grade 9, Franklin County High School, Rocky Mount, Virginia
Jenny Kaplan, Grade 7, Castilleja Middle School, Palo Alto, California
Alex Chen, Grade 7, Odle Middle School, Bellevue, Washington
Caleb Ho, Grade 11, Monterey Bay Academy, Watsonville, California
Tommy Johnson, Grade 9, Western Albemarle High School, Crozet, Virginia
Amey Adkins, Grade 9, Franklin County High School, Rocky Mount, Virginia
Zimran Douglas, Grade 12, Wingate High School, Brooklyn, New York
Chaim Bloom, Grade 10, Akiba Hebrew Academy, Merion, Pennsylvania
Lindsay Burdett, Grade , Redmond High School, Redmond, Oregon
Alison Miller, Grade 6, homeschooled, Niskayuna, New York
Michael Moyer, Grade 10, The Way Home School, Carlisle, Pennsylvania
Emily Castor, Grade , Granada High School, Livermore, California
Jennifer Liang, Grade 8, Odle Middle School, Bellevue, Washington
Brad Hanson, Grade , Redmond High School, Redmond, Oregon
Sarah Fladwood and Peter Hoover and Kasey Jones, Grade , Redmond High School, Redmond, Oregon
Alex Chernyavsky, Grade , Akiba Hebrew Academy, Merion, Pennsylvania
Cally Whitman, Grade , Redmond High School, Redmond, Oregon
Donnie Campbell, Grade , Redmond High School, Redmond, Oregon
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