Suppose you have a perpendicular bisector of a chord passing through the center of a circle. The perpendicular from the center of the circle bisects the chord giving the chord two equal sides.Are the two sides guaranteed to be perpendicular??

Any help would be greatly appreciated.

Suppose you have a perpendicular bisector of a chord passing through the center of a circle. The perpendicular from the center of the circle bisects the chord giving the chord two equal sides.Are the two sides guaranteed to be perpendicular??

Any help would be greatly appreciated

Your statement "Suppose you have a perpendicular bisector of a chord" passing through the center of a circle defines that the chord, or any of its segments, are perpendicular to the radius line passing through the circle's center.

I'm confused???

The chord is a straight line. When the bisector of the cord divides it into two equal parts, how can the two sides be perpendicular.

Reminder: perpendicular means meeting at right angles -- like a wall meets a floor.

Suppose you have a perpendicular bisector of a chord passing through the center of a circle. The perpendicular from the center of the circle bisects the chord giving the chord two equal sides.Are the two sides guaranteed to be perpendicular??

I am assuming that you mean "Are the two sides guaranteed to be perpendicular to the bisector, not each other.

To determine whether the two sides of a chord, bisected by a perpendicular from the center of a circle, are guaranteed to be perpendicular, we need to consider the properties of a circle.

Let's break down the problem step by step:

1. A perpendicular bisector is a line that is perpendicular to a given line and passes through its midpoint.
2. In this case, we have a chord (a line segment that connects two points on the circumference of a circle) and a perpendicular bisector passing through its midpoint and the center of the circle.
3. Since the perpendicular bisector passes through the center of the circle, it divides the chord into two equal parts (halves).
4. The two halves of the chord will be equal in length due to the midpoint property of the perpendicular bisector.
5. Now, to determine if the two halves are guaranteed to be perpendicular, we need to use the property of a circle that states: "The line segment joining the center to any point on the circumference of a circle is called a radius, and it is perpendicular to the tangent line at that point."
6. In this scenario, the line segment from the center of the circle to the midpoint of the chord is a radius, and the chord is a tangent line at that point.
7. According to the property mentioned in step 5, the radius (perpendicular from the center to the midpoint of the chord) is perpendicular to the chord.
8. Therefore, the two halves of the chord, bisected by a perpendicular from the center of the circle, will indeed be guaranteed to be perpendicular.

In conclusion, if you have a perpendicular bisector of a chord passing through the center of a circle, the perpendicular from the center will bisect the chord into two equal parts, and those two parts will be guaranteed to be perpendicular.