9 Answered Questions for the topic Euclidean Geometry

Euclidean Geometry Geometry College Geometry

07/27/21

Use the trigonometric form of Ceva’s theorem to prove that the three Cevian lines in the definition of isogonal conjugate are concurrent.
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Euclidean Geometry

03/31/21

Prove that ABE is equal to DCE
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Euclidean Geometry

04/30/20

Proving 3 points determine a unique plane
I'm trying to prove the early "Postulates" (#6-10 or so) of Euclidean geometry. I'm trying to rely on Euclid's 5 and his definitions - only. I don't want to demonstrate using some sort of... more
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Euclidean Geometry Geometry Trigonometry Triangle

03/19/19

Does a triangle always have a point where each side subtends equal 120° angles?
Is there a point $O$ inside a triangle $\ riangle ABC$ (any triangle) such that the angle $\\angle{AOB} = \\angle{BOC} = \\angle{AOC}$? What do we call this point?
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Euclidean Geometry Geometry Trigonometry

03/18/19

How to prove $\\cos \\frac{2\\pi }{5}=\\frac{-1+\\sqrt{5}}{4}$?
I would like to find the apothem of a regular pentagon. It follows from $$\\cos \\dfrac{2\\pi }{5}=\\dfrac{-1+\\sqrt{5}}{4}.$$ But how can this be proved (geometrically or trigonometrically)?
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Euclidean Geometry

09/15/18

Segment AB is given with midpoint m. Also, c is a point between A and M. Prove, cm=(1/2)(CB-CA)
Segment AB is given with midpoint m. Also, c is a point between A and M. Prove, cm=(1/2)(CB-CA)
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Euclidean Geometry

05/04/18

Which undefined geometric term is best described as a location on a coordinate plane that is designed by an ordered pair (x,y)
Which undefined geometric term is best described as a location on a coordinate plane that is designed by an ordered pair (x,y)
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03/08/18

finding GCD using Euclidean
i) Use the Euclidean Algorithm to calculate the greatest common divisor of 95658 and 48685.Clearly outline all the steps in the algorithm. (ii) Reverse Euclid’s Algorithm in (i) to find integers x... more
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Euclidean Geometry

09/02/16

How would I construct a line perpendicular to a point on a line
If given a total of 3 lines or circles to work with. One of the three objects must be the perpindicular line itself. So max of 2 circles. Max 3 lines. But only 3 total of a combination.    Assume... more
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