Carcass wrote:

P, Q, and R are three points in a plane, and R does not lie on line PQ. Which of the following is true about the set of all points in the plane that are the same distance from all three points?

A) It contains no points.

B) It contains one point.

C) It contains two points.

D) It is a line.

E) It is a circle.

Practice Questions

Question: 23

Page: 463

Difficulty: hard

Tricky question!!!I thought I'd create some images to go along with Carcass' solution.

Let's first consider 2 points (P and Q)

One obvious point that is equidistant from P and Q is this point...

Also recognize that, if we draw two circles of

equal radii with their centers at PQ, the 2 points of intersection will also be equidistant from P and Q

In fact, all points on this red line are equidistant from P and Q. The red line (as Carcass mentioned above) is the perpendicular bisector of points P and Q.

At this point, let's add a 3rd point (R) and draw the perpendicular bisector of points R and P in blue. All points on the blue line will be equidistant from R and P.

So, the green point (where the blue line and red line intersect) must be equidistant from R and P,

AND it must equidistant from P and Q.

So, that green point must be equidistant from P, Q and R

Since there is only 1 such green point, the correct answer is B.

Cheers,

Brent

_________________

Brent Hanneson – Creator of greenlighttestprep.com

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