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The perpendicular bisector of a chord is a line passing through the center of the circle such that it divides the chord into two equal parts and meets the chord at a right angle. A circle is a 2D figure without corners or edges such that all the points on the boundary are equidistant from the center. The line segment connecting the center with ...
Consider a chord AB of a circle with center O, as shown below. Let C be the mid-point of AB: Proof: If we are able to prove that OC is perpendicular to AB, then we will be done, as then OC will be the perpendicular bisector of AB. Compare triangles OAC and OBC: 1. OA = OB (radii of the same circle) 2. OC = OC (common)
Answer. Since 𝑀 is the center of the circle and line 𝑀 𝐷 bisects chord 𝐴 𝐵 at 𝐶, we can apply the chord bisector theorem, which states that if we have a circle with center 𝑀 containing a chord 𝐴 𝐵, then the straight line that passes through 𝑀 and bisects chord 𝐴 𝐵 is perpendicular to 𝐴 𝐵. Hence, we can ...
A chord is a line whose endpoints lie on the circle. The perpendicular bisector of the chord is a line that crosses the line at 90° (perpendicular) and cuts it in half (bisector). This perpendicular bisector of the chord passes through the center of the circle.
- What Is The Perpendicular Bisector of A chord?
- Why Is It Important?
- Conclusion
- FAQ
A perpendicular bisector of a chord is a line that passes through the midpoint of two points on a curve and intersects the curve at right angles. For example, if you have two points on a circle, A, and B, then the perpendicular bisector of their chord (the line segment AB) will pass through the midpoint of AB and intersect the circle at right angle...
The perpendicular bisector of a chord is an essential tool in understanding many geometric concepts. By having an understanding of how chords work with respect to their respective circles or curves, students can gain insight into more complex topics such as conic sections and transformations. Knowing how to calculate this information can also help ...
In conclusion, the perpendicular bisector of a chord is an important concept for anyone studying geometry or related fields. It helps us determine properties about circles or curves by passing through their midpoints at right angles. It’s also useful for finding out whether lines are parallel or if three points are collinear. Understanding this con...
What is a perpendicular bisector in geometry?
A perpendicular bisector is a line that passes through the midpoint of two points on a curve and intersects the curve at right angles. It can be used to find out whether lines are parallel, if three points are collinear, and various other properties of shapes or equations.
How do you prove a perpendicular bisector of a chord?
In order to prove that a line is the perpendicular bisector of a chord, you have to show that it passes through the midpoint and intersects the curve at right angles.
What is perpendicular to the chord?
A perpendicular line to the chord is a line that passes through the midpoint of two points on a curve and intersects the curve at right angles.
Aug 16, 2020 · A chord is any line drawn across a circle, from one point on the circumference to another: The perpendicular bisector of a chord is the line that cuts the chord in half, at a right angle: The perpendicular bisector of a chord passes through the centre of the circle. This theorem is covered in this video on circle theorems:
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Chords, intercepted Arcs & Theorems. The perpendicular bisector of a chord. contains the circle's center. divides the chord into two congruent segments (bisects the chord) is perpendicular to the chord.
