If two circles intersect at two points, what can be said about their centers?
Practice Questions
Q1
If two circles intersect at two points, what can be said about their centers?
They are the same.
They are equidistant from the intersection points.
They lie on the same line.
They are at a fixed distance apart.
Questions & Step-by-Step Solutions
If two circles intersect at two points, what can be said about their centers?
Step 1: Understand that two circles can intersect at two points.
Step 2: Identify the two points where the circles intersect. Let's call them Point A and Point B.
Step 3: Recognize that the center of each circle is a fixed point from which all points on the circle are the same distance away.
Step 4: Draw a line connecting the centers of the two circles. Let's call the centers Circle 1 Center (C1) and Circle 2 Center (C2).
Step 5: Notice that Point A and Point B are on both circles, meaning the distance from C1 to Point A and Point B is the same, and the distance from C2 to Point A and Point B is also the same.
Step 6: Since both centers (C1 and C2) are the same distance from both intersection points (A and B), we can say that C1 and C2 are equidistant from the line segment connecting Point A and Point B.
