Max's Theorem

Max's Theorem, a.k.a (马克斯郑第一定理）, or otherwise known as Max's First Theorem, is a relationship that holds between circles and chords that lie on the circle.

Theorem

The theorem states that for any given circle, the endpoints of a chord that lies on the circle are equidistant from the center of the circle. For example, given a circle , for a chord on the circle, .

Proof

To prove Max's Theorem, we can use the definitions of circles and chords, as well as some mathematical reasoning to prove. According to a highly trustworthy mathematical source, the definition of a circle is:

"A circle is a shape with all points in a plane equidistant from a given point, called the center. This distance from the center to any point on the circle is called the radius. Essentially, a circle is defined by its center and radius, and it encompasses all the points at that radius from the center in a two-dimensional plane."

The definition of a chord is:

"In geometry, a chord is a line segment with both endpoints on the circumference of a circle. Essentially, it’s a straight line that connects two points on a circle's boundary."

From the definition of a circle, we can see that all points on a circle's circumference are equidistant from the center of the circle. Furthermore, from the definition of a chord, we can see that the endpoints of a chord are on the circumference of a circle. Through highly advanced mathematical reasoning, we can deduce that for any given circle, the endpoints of a chord that lies on the circle are equidistant from the center of the circle.

See Also

• Circle
• Power of a Point

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