If two circles intersect at two points, which of the following statements is tru

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Question: If two circles intersect at two points, which of the following statements is true? (2021)

Options:

The centers of the circles are equidistant from the intersection points.
The line joining the centers of the circles passes through the intersection points.
The circles are tangent to each other.
The area of intersection is always a triangle.

Correct Answer: The centers of the circles are equidistant from the intersection points.

Exam Year: 2021

Solution:

The centers of the circles are equidistant from the intersection points, making option 0 true.

If two circles intersect at two points, which of the following statements is true? (2021)

The centers of the circles are equidistant from the intersection points.
The line joining the centers of the circles passes through the intersection points.
The circles are tangent to each other.
The area of intersection is always a triangle.

If two circles intersect at two points, which of the following statements is true? (2021)

Step 1: Understand that two circles can intersect at two points.
Step 2: Identify the two intersection points where the circles meet.
Step 3: Recognize that the center of each circle is a fixed point.
Step 4: Measure the distance from each center to the two intersection points.
Step 5: Realize that the distance from the center of the first circle to both intersection points is the same as the distance from the center of the second circle to those same points.
Step 6: Conclude that the centers of the circles are equidistant from the intersection points.

Circle Intersection Properties – When two circles intersect, the line segment connecting their centers is perpendicular to the line segment connecting the intersection points.