Because the definition of an angle consists of two rays at a fixed point. The ray is infinitely extended, so the definition of the central angle does not say that two sides intersect with the circle, because the ray must intersect with the circle, and the angle with the side as a line segment is not the central angle.

The relationship between degree and percentage of fan-shaped central angle is: degree of central angle = percentage *360 degrees.

Let the Xuan length be a, the arc height be h, the central angle be α, the arc length be l, and the circle radius be r.

h*2R=a？ /4

R=a？ /(8 hours)

sinα=a/[a？ /8h] =8h/a

∴ 2α = arcsine (8h/a)- unit: radian.

L=2α*a？ /8h=αa？ /4h

Extended data:

Understand:

(1) Equal arc and equal central angle

(2) When the fillet of the vertex at the center of the circle is divided into 360 parts, the central angle of each part is 1.

(3) Because the arcs with equal central angles in the same circle are equal, the whole circle is equally divided into 360 parts. At this time, each arc thus obtained is called the arc of 1.

(4) The degrees of the central angles are equal to the degrees of the arcs they subtend.

Baidu encyclopedia-center corner