2. Letโs Learn
Given a circle with center P. Let us
consider โ ๐ด๐๐ต. It is called a central angle of the
circle. The vertex of the angle is point P.
Let us considered points A, B and C on the
circle. The union of points A, B and all points of the
circle in the interior of โ ๐ด๐๐ต is called minor arc. To
denote minor arc we write ๐จ๐ฉ.
The major arc is the union of points A, B
and all the points on the circle in the exterior of
โ ๐ด๐๐ต. To denote major arc, we write ๐ด๐ถ๐ต.
3. In each case both, A and C are the end
points of both minor and major arcs.
Arcs of a circle and the central angle that
intercept them are related in special way.
The measure of an arc, in degrees, is
numerically equal to the measure of the
corresponding central arc.
So, if mโ ๐ด๐๐ต = 60ยฐ, the measure of the
corresponding minor arc ๐ด๐ต is also 60ยฐ.
The degree measure of a major arc is
equal to 360ยฐ minus the measure of the
corresponding minor arc.
4. If A and B are the endpoints of a diameter,
then we have two arcs each of which is called
semicircle or half circle.
The degree measure of a semicircle is 180ยฐ.
The entire circle has an arc measure of 360ยฐ.
The degree measure of a major arc is equal to 360ยฐ
minus the measure of the corresponding minor arc.
In the same or congruent circles, two arcs
are congruent if they have the same measure.
Thus, if m๐ถ๐ต โ m๐ท๐ธ, then ๐ถ๐ต โ ๐ท๐ธ.
Also, โ ๐ถ๐ด๐ต โ โ ๐ท๐ด๐ธ.