Question

Draw two points $A$ & $B$ and several circles that pass through $A$ and $B$. Locate the centers of these circles. On the basis of your experiment, complete the following statement:

The centers of all circles passing through $A$ and $B$ lie on ______.

Write an argument to support your statement.

Short answer

The centres of all circles passing through $A$and $B$ lie on a straight line.

Step-by-step solution

Step 1. Given information. 

Circles passes through two points A and B.

Step 2. Concept used.

Co-linear centers.

Step 3. Find value.

The points of centres of circles are co-linear, which are passing through the two intersection points, namely A and B.

Therefore, the centres of all the circles passing through A and B lie on a straight line.