#### The following multiple-select question, explained here in hopes of helping geometry students in Maryland and Illinois prepare for the PARCC test near the end of this school year, appears on the released version of PARCC’s Spring 2015 test in geometry, here:

Select from the dropdown menus to correctly complete each sentence.

The set of all points in a plane that are equidistant from a given point is called a {square, sphere, segment, circle}.

The given point is called the {square, sphere, segment, circle}.

*[sic]*

## Resources for further study

**Purple Math**, developed by Elizabeth Stapel, a math teacher from the St Louis area, has a page on the limited use circles have in algebra, given the inescapable fact that a circle is not a function (it fails the vertical line test).

The **Khan Academy**, developed by Sal Khan, an engineer who has several videos dealing with circles and their properties, beginning here. The landing page also features links to proofs of various theorems involving circles, which you may be required to know for the PARCC geometry test.

Chapter 10 of the book * Geometry for Enjoyment and Challenge* by Richard Rhoad

*et al*, all teachers from Illinois, features the following definitions related to circles:

A circle is the set of all points in a plane that are a given distance from a given point in the plane. The given point is the center of the circle, and the given distance is the radius. A segment that joins the center to a point on the circle is also called a radius.

(Richard Rhoad, George Milauskas, and Robert Whipple. *Geometry for Enjoyment and Challenge*, new edition. Evanston, Ill.: McDougal Littell, a division of Houghton Mifflin Company, 1991. The book is used in several geometry classes taught in Illinois high schools.)

## Analysis of this question and online accessibility

The question measures knowledge of the Common Core standards it purports to measure and tests students’ understanding of the definition of a circle and its radius. It is considered to have a low cognitive demand.

The question can be tested online and should yield results that are as valid and reliable as those obtained on paper.

No special accommodation challenges can be identified with this question, so the question is considered fair.

## Challenge

Prove that if two different tangents to the same circle intersect at a common point (outside the circle), the line segments between that point and the two points of tangency have the same length (help here or here).

## Purpose of this series of posts

Voxitatis is developing blog posts that address every algebra 1 question released to the public by the Partnership for Assessment of Readiness for College and Careers, or PARCC, in order to help students prepare to take the test this spring.

Our total release will run from February 27 through March 15, with one or two questions discussed per day. Then we’ll move to geometry at the end of March, algebra 2 during the first half of April, and eighth grade during the last half of April.