Let ABC be an isosceles triangle, where AB AC. Suppose that M is a point on the side AB such that AB- MB = AM2. Suppose also that AM = BC. Prove that the angle ZABC is twice ZBAC. [Hint: Consider the circumcircle O of AMC. Show that BC is tangent to O. Use this to show that ZCMB = ZCBM . You are encouraged to use propositions from Books 1, 2, & 3 from Euclid's Elements.] Draw a picture to help support your proof.
Let ABC be an isosceles triangle, where AB AC. Suppose that M is a point on the side AB such that AB- MB = AM2. Suppose also that AM = BC. Prove that the angle ZABC is twice ZBAC. [Hint: Consider the circumcircle O of AMC. Show that BC is tangent to O. Use this to show that ZCMB = ZCBM . You are encouraged to use propositions from Books 1, 2, & 3 from Euclid's Elements.] Draw a picture to help support your proof.
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 1CT
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![Let ABC be an isosceles triangle, where AB AC. Suppose that M is a point
on the side
AB such that AB- MB = AM2. Suppose also that AM = BC. Prove that the angle ZABC is
twice ZBAC. [Hint: Consider the circumcircle O of AMC. Show that BC is tangent to O.
Use this to show that ZCMB = ZCBM . You are encouraged to use
propositions from Books 1,
2, & 3 from Euclid's Elements.] Draw a picture to help support your proof.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb2707a03-8914-44d9-b3b0-567da8e5c887%2F01592783-0a67-491c-bb37-1eb157662b8f%2Fls7riwh.png&w=3840&q=75)
Transcribed Image Text:Let ABC be an isosceles triangle, where AB AC. Suppose that M is a point
on the side
AB such that AB- MB = AM2. Suppose also that AM = BC. Prove that the angle ZABC is
twice ZBAC. [Hint: Consider the circumcircle O of AMC. Show that BC is tangent to O.
Use this to show that ZCMB = ZCBM . You are encouraged to use
propositions from Books 1,
2, & 3 from Euclid's Elements.] Draw a picture to help support your proof.
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