Question

to show that infinite circles can be drawn passing through two points

Answer 1

As long as you can change the size of the circle, then an infinite number of circles can be made to pass through 2 points. Infinite number of circles can be drawn passing through two given points if not otherwise mentioned that the two given points are the end points of a diameter of a circle.

Answer 2

To show that infinite circles can be drawn passing through two points, we can use the fact that the perpendicular bisector of a line segment passes through its midpoint.

Suppose we have two points, A and B. We can draw the line segment AB connecting these two points. Then, we can construct the perpendicular bisector of AB. This perpendicular bisector will pass through the midpoint of AB, which we will call point M.

Now, let C be any point on the perpendicular bisector of AB, such that C is not equal to M. We can draw the line segments AC and BC. Since C lies on the perpendicular bisector of AB, we know that AC and BC are congruent and perpendicular to AB.

Therefore, we have a right triangle with legs AC and BC and hypotenuse AB. By the Pythagorean theorem, we know that $AC^2 + BC^2 = AB^2.$

Now, consider the circle with diameter AB. This circle will pass through points A and B. Since $AC^2 + BC^2 = AB^2$we know that C lies on the circle with diameter AB. Therefore, any point on the perpendicular bisector of AB, other than the midpoint M, lies on the circle passing through points A and B.

Since the perpendicular bisector of AB is a line, there are an infinite number of points on this line other than M. Therefore, there are infinite circles passing through points A and B.

Learn more about triangle :

https://brainly.in/question/54231692

Learn more about perpendicular :

https://brainly.in/question/14657202

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