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daser333 [38]
3 years ago
9

Mateo is constructing an equilateral triangle inscribed in a circle with center P. He draws the diameter of the circle through c

enter P using a straight edge. What is his next step?
A. Use a straight edge and compass to find lines perpendicular to the endpoints of the diameter.
B. Open his compass to a width equivalent to the radius of the circle.
C. Open his compass to a width equivalent to the diameter of the circle.
D. Use a straight edge and compass to find the perpendicular bisector of the diameter.
Mathematics
1 answer:
spin [16.1K]3 years ago
7 0
<span>Let,
diameter = segment AB through center P.
Set the compass to the radius PB, at B and draw two little arcs that intersect the circumference of the circle at C and D.
Then Triangle ACD will be an equilateral triangle inscribed in the given circle.
Hence,
The right option is :
</span><span>B. Open his compass to a width equivalent to the radius of the circle.</span>
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De moirve's <br> (√3-i ÷ √3+i)^6 = 1
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(√3 - <em>i </em>) / (√3 + <em>i</em> ) × (√3 - <em>i</em> ) / (√3 - <em>i</em> ) = (√3 - <em>i</em> )² / ((√3)² - <em>i</em> ²)

… = ((√3)² - 2√3 <em>i</em> + <em>i</em> ²) / (3 - <em>i</em> ²)

… = (3 - 2√3 <em>i</em> - 1) / (3 - (-1))

… = (2 - 2√3 <em>i</em> ) / 4

… = 1/2 - √3/2 <em>i</em>

… = √((1/2)² + (-√3/2)²) exp(<em>i</em> arctan((-√3/2)/(1/2))

… = exp(<em>i</em> arctan(-√3))

… = exp(-<em>i</em> arctan(√3))

… = exp(-<em>iπ</em>/3)

By DeMoivre's theorem,

[(√3 - <em>i </em>) / (√3 + <em>i</em> )]⁶ = exp(-6<em>iπ</em>/3) = exp(-2<em>iπ</em>) = 1

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