Question

Casey constructed this figure by using a compass and a straightedge to draw circle O and diameter PQ. She then used a compass to draw two arcs. She labeled the points where those arcs intersect the circle M and N, and she drew the chords that form the triangle.

If ΔMNP is equilateral, how did Casey draw the arcs that defined points M and N?

A.
She used a compass centered at P with a radius set equal to PQ.
B.
She used a compass centered at O with a radius set equal to PO.
C.
She used a compass centered at Q with a radius set equal to PO.
D.
She used a compass centered at P with a radius set equal to (PQ).
E.
She used a compass centered at Q with a radius set equal to PQ.

Answer 1

D) she used a compass at P with a radius set equal to 3/4(PQ)

Explanation:

Step 1

She used a compass at P with a radius set equal to 3/4PQ .

Step 2

Since if ∆MNP is equilateral triangle so, PM=PN=MN

Since O is center then PO=OQ

And let R is the mid point of MN.

So, R is also mid point of OQ.

Hence, she used a compass at P with a radius set equal to 3/4(PQ)