eybrj2 wrote:
Which of the figures below can be inscribed in a circle?
(A) I only
(B) III only
(C) I & III only
(D) II & III only
(E) I, II & III
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Bunuel, you never got your alternative solution...so here goes!!
In order for it to possible to inscribe a shape in a circle, we need to be able to find a point that is equidistant from the vertices. That point will be the center of the circle and the vertices will therefore all reside on the circumference. Lets look at our shapes.
I: If we draw a vertical line through the shape, all the points on the line are equidistant from the two upper vertices and also equidistant from the two lower vertices. If we pick the point on the line that is where the line meets the lower base (the red point), it will be closer to the to two lower vertices than it is to the two upper vertices. And if we pick the point on the line that is where the line meets the upper base (the green point), it will be closer to the two upper vertices than it is to the two lower vertices. That means that there must be some point between those two points where we are equidistant from the upper and lower vertices (the purple point). I works.
For II and III, I think we can simply visualize whether there's a way to draw a circle that hits all for vertices. If you get stuck and would benefit from a more thorough response, say the word and I'll supplement this post. For now, I'll go with II doesn't work and III does.
Answer choice C.
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