"Relationship between Circumferential Angle and Central Angle" Circle PPT Courseware

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"Relationship between Circumferential Angle and Central Angle" Circle PPT Courseware

think about it

A circumferential angle has its vertex on a circle, and its two sides have another intersection point with the circle. An angle like this is called a circumferential angle.

Determine the circumferential angle by analogy with the central angle of a circle

In congruent or equal circles, equal arcs subtend equal central angles.

What is the relationship between the angles subtended by equal arcs in congruent or equal circles?

In order to solve this problem, we first explore the relationship between the circumferential angle and the central angle of an arc.

1. First consider a special case:

When the center (O) of the circle is on one side (BC) of the circumferential angle (∠ABC), the relationship between the circumferential angle ∠ABC and the central angle ∠AOC is.

∵∠AOC is the exterior angle of △ABO,

∴∠AOC=∠B+∠A.

∵OA=OB，

∴∠A=∠B.

∴∠AOC=2∠B.

Relationship between circumferential angle and central angle

What will happen if the center of the circle is not on one side of the angle?

2. When the center (O) of the circle is inside the circumferential angle (∠ABC), what is the relationship between the circumferential angle ∠ABC and the central angle ∠AOC?

Teacher’s tip: Can it be transformed into a situation of 1?

∠ABD =1/2∠AOD, ∠CBD =1/2∠COD,

∴ ∠ABC =1/2∠AOC.

The circumferential angle subtended by an arc is equal to half of the central angle subtended by it.

Expand and turn your heart into action

1. As shown in the figure, in ⊙O, what is the relationship between the sizes of ∠B, ∠D and ∠E? Why?

2. Think about it, is there such a conclusion in equal circles?

The circumferential angles subtended by congruent arcs or congruent arcs are equal;

In congruent or congruent circles, equal arcs subtended by equal circumferential angles are also equal.

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"The Relationship between Circumferential Angle and Central Angle" Circle PPT Courseware 5:

"The Relationship between Circumferential Angle and Central Angle" Circle PPT Courseware 5 Knowledge Review Circumferential Angle: The vertex is on the circle, and its two sides have another intersection with the circle. An angle like this is called a circumferential angle. Circumferential Angle Theorem The circumference of a circle subtended by an arc An angle is equal to half of the central angle of the circle it subtends. Health...

"The Relationship between the Circumferential Angle and the Central Angle" Circle PPT Courseware 4:

"The Relationship between Circumferential Angle and Central Angle" Circle PPT Courseware 4 Circumferential Angle Definition: An angle whose vertex is on a circle and both sides intersect with the circle is called a circumferential angle. Features: ① The vertex of the angle is on the circle. ② Both sides of the angle intersect with the circle Intersect. Hands on the relationship between the circumferential angle and the central angle of the circle subtended by the same arc..

"The Relationship between Circumferential Angle and Central Angle" Circle PPT Courseware 3:

"The Relationship between Circumferential Angle and Central Angle" Circle PPT Courseware 3 Knowledge Review 1. A circle is an axially symmetrical figure. The symmetry axis of a circle is any straight line passing through the center of the circle. It has countless symmetry axes. 2. A circle is also a centrally symmetrical figure. It The center of symmetry is the center of the circle. 3. The vertex is at the center of the circle..

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Update Time: 2024-10-19

This template belongs to Mathematics courseware Beijing Normal University Ninth Grade Mathematics Volume 2 industry PPT template

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