2019 AMC 10A Problems/Problem 6

Revision as of 19:51, 9 February 2019 by Argonauts16 (talk | contribs) (Solution)

Problem

For how many of the following types of quadrilaterals does there exist a point in the plane of the quadrilateral that is equidistant from all four vertices of the quadrilateral?

  • a square
  • a rectangle that is not a square
  • a rhombus that is not a square
  • a parallelogram that is not a rectangle or a rhombus
  • an isosceles trapezoid that is not a parallelogram

$\textbf{(A) } 1 \qquad\textbf{(B) } 2 \qquad\textbf{(C) } 3 \qquad\textbf{(D) } 4 \qquad\textbf{(E) } 5$

Solution

This question is simply asking how many of the listed quadrilaterals are cyclic. A square, a rectangle, and an isosceles trapezoid (that isn't a parallelogram) are all cyclic, and the other two are not. Thus, the answer is $3 \implies \boxed{\textbf{(C)}}.$

See Also

2019 AMC 10A (ProblemsAnswer KeyResources)
Preceded by
Problem 5
Followed by
Problem 7
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All AMC 10 Problems and Solutions

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