А 4.7 Let ABC be an equilateral triangle in scribed in a circle. Let D, E be the mid points of two sides, and extend DE to meet the circle at F. Prove that E divides F the segment DF in extreme and mean ratio, ie. the rectangle EF x DF equals the square DE. Hint: Use (III.35)

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter8: Applications Of Trigonometry
Section8.2: The Law Of Cosines
Problem 48E
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Use the following proposition (Euclid's Elements Book III, Prop 35) for assistance: "If in a circle two straight lines cut one another, the rectangle contained by the segments of the one is equal to the rectangle contained by the segments of the other"

А
4.7 Let ABC be an equilateral triangle in
scribed in a circle. Let D, E be the mid
points of two sides, and extend DE to
meet the circle at F. Prove that E divides
F
the segment DF in extreme and mean
ratio, ie. the rectangle EF x DF equals
the square DE. Hint: Use (III.35)
Transcribed Image Text:А 4.7 Let ABC be an equilateral triangle in scribed in a circle. Let D, E be the mid points of two sides, and extend DE to meet the circle at F. Prove that E divides F the segment DF in extreme and mean ratio, ie. the rectangle EF x DF equals the square DE. Hint: Use (III.35)
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