On the same plane, the set of points whose distance to a fixed point is equal to a fixed length is called a circle. According to the definition of a circle, we can construct an isosceles triangle by connecting the radii inside the circle. For example, 1, DO=DE is obtained by using the radius equation, and then ∠E=∠DOE, and the conclusion can be drawn according to the nature of the triangle outer angle.
The vertical diameter theorem is a theorem in mathematical geometry (circle). Its popular expression is: the diameter perpendicular to the chord bisects the chord and bisects the two arcs opposite to the chord. A right triangle can be formed by using a circle as the chord center distance, and the chord length, radius or chord center distance can be calculated by using Pythagorean theorem.
In a circle, the circumferential angle of the diameter is 90 degrees. When a diameter appears in a circle, the circumferential angle opposite to the diameter is often constructed. Example 3 mainly investigates the calculation of the angle inside the circle. Connecting BD not only constructs the circumferential angle opposite to the diameter, but also constructs the circumferential angle equal to the same arc.
The tangent of the circle passes through the outer end of the radius and is perpendicular to the radius. When a tangent line appears on a circle, we need to connect the center of the circle with the intersection point on the circle, so as to get verticality.
The determination of tangent is the high-frequency test center of the senior high school entrance examination. There are two main ways to judge the tangent: (1) There is a definite intersection between a straight line and a circle, and the verticality can be proved by the connecting radius; (2) There is no definite intersection point between a straight line and a circle. If it is vertical, it is proved to be equal to the radius. Connecting OD proves that OD is perpendicular to DF.
The center of a triangle is the center of the inscribed circle of the triangle, which reaches the intersection point of the bisectors of the three internal angles of the triangle. Therefore, if this problem is related to BN, we can get ∠ 1=∠2 and ∠ 3 = ∠ 4.