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The construction of the regular pentagon is equivalent to the construction of the point in the unit circle with x coordinate x1 = the square root of 5 - 1 divided by 4. Use this to construct a regular pentagon that has all its vertices inside the unit circle. Write a construction protocol and justify all your construction steps. How do I construct the square root of 5-1?

  • geometry -

    You must mean
    √5 - 1

    draw a square ABCD with sides 2 , where A and B are the endpoints of the base
    Extend the length of the base to the right

    Draw a vertical MN where M is the midpoint of AB and N is the midpoint of CD
    You should see a right-angled triangle with legs AB = 1 and MN = 2
    by Pythagoras AN = √5

    Use your compass, centre at A and radius AN , draw an arc to cut the entension of AB at P
    so AP = √5
    and MP = √5 - 1

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