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

Description

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

Definition of circumferential angle: An angle whose vertex is on a circle and both sides intersect the circle is called a circumferential angle.

Characteristics: ① The vertex of the angle is on the circle. ② Both sides of the angle intersect the circle.

The relationship between the circumferential angle and the central angle of a circle subtended by the same arc

Hands-on operation: In the same circle, draw the circumferential angle (∠ACB) and the central angle (∠AOB) of the same arc, and measure the sizes of the circumferential angle and central angle you drew.

Note: The position of the center and the angle of the circle

basic training

1. Which of the following propositions is true ( )

(A) The angle of the vertex on the circumference is called the circumferential angle

(B) The arc subtended by a 60º circumferential angle is 30º

(C) The circumferential angle subtended by an arc is equal to the central angle subtended by it

(D) The angle subtended by an arc of 120º is 60º

2. As shown in the figure on the right, in ⊙O, ∠ACB = 130º, then ∠AOB=______.

3. Find the measure of ∠α in the circle.

4. As shown in the figure, OA⊥BC, ∠AOB=50°, then ∠CDA=25°

5. In a circle with radius R, the circumferential angle subtended by a chord of length R is 30° or 150°

Class summary

1. What new knowledge did you learn in this lesson?

2. What knowledge did you apply?

3． What methods were used to solve problems during the learning process?

Improve ability

1. As shown in the figure, OA, OB, and OC are all radii of ⊙0, ∠AOB=2∠BOC

What is the relationship between the size of ∠ACB and ∠BAC? Why?

2. As shown in the figure, points A, B, C, D, and E are all on ⊙0, then what degree is ∠A+∠B+∠C+∠D+∠E equal to? Why?

Analysis: The sum of the arcs subtended by the five circumferential angles ∠A∠B∠C∠D∠E is exactly a circle, and the central angle subtended by a circle is 360°.

So: ∠A+∠B+∠C+∠D+∠E=180°

3. As shown in the figure, in ⊙O, BC=2DE, ∠BOC=84°, find the degree of ∠A.

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Update Time: 2024-07-02

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