You are constructing a tangent line from a point outside a given circle to the circle. you have drawn the circle, a point outside the circle and connected the center of the circle to the point outside the circle. you found the midpoint of the segment. next you must use your compass. after you set it, where should you put the point? a) the center of the circle b) the point outside the circle c) the midpoint of the segment d) the intersection of the segment and the circle

  C)  The midpoint of the segment

Step-by-step explanation:

The point of tangency is the intersection of the original circle and the semicircle whose diameter is the segment from the original circle center to the external point. The step being described is the step where the semicircle is being drawn, so the point of the compass will be at the midpoint of the segment.

3. parallelogram

step-by-step explanation:

we turn each of our sides into direction vectors

ab=b-a=(3 - 7, 1 - 0) = (-4, 1)

bc=c-b=(1,6)

cd=d-c=(4,-1)

da=a-d=(-1,-6)

we see how the opposite sides have negated direction vectors; this is characteristic of a parallelogram.   we have congruent sides ab=cd and bc=da with unequal lengths because 1^2+6^2 is different from (-4)^2+1^2.   so it's not a square or a rhombus.  

we check the dot product of direction vectors of adjacent sides.   we have

ab dot bc = -4(1) + 1(6) = 2

that's not zero so the sides are not perpendicular.   we've ruled out rectangle.

the direction vectors indicate two pairs of congruent parallel sides, so we choose parallelogram over trapezoid.