- #1

mahblah

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- Homework Statement
- Four points in the plane are given, not all on the same straight line, and not all on a circle. How many straight lines and circles can be drawn which are equidistant from these points?

- Relevant Equations
- by distance from a point P to a circle c with center O we mean the lenght of the segment PQ, where Q is the point where the ray from O in the direction OP meets c

Hi, i'm trying to solve this problem.

It's exercise 3 on page 5 from this book:

Challenging mathematical problem with elementary solutions

The solution is on page 41:

I'm OK with the 4 circles in case 1: i can pick (inside/outside):

ABC + D,

ABD + C,

ADC + B,

BCD + A.

What i cannot understand is how there can be 4 straight lines in case 1:

if three points stand on one side of the equidistant line, these point must be collinear, and so there is only one possible straight line (i cannot re-arrange them!)

where am I wrong?

thanks

It's exercise 3 on page 5 from this book:

Challenging mathematical problem with elementary solutions

The solution is on page 41:

I'm OK with the 4 circles in case 1: i can pick (inside/outside):

ABC + D,

ABD + C,

ADC + B,

BCD + A.

What i cannot understand is how there can be 4 straight lines in case 1:

if three points stand on one side of the equidistant line, these point must be collinear, and so there is only one possible straight line (i cannot re-arrange them!)

where am I wrong?

thanks