"Central Angle and Circumferential Angle" PPT courseware

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"Central Angle and Circumferential Angle" PPT courseware

1. The angle whose vertex is at the center of the circle is called ________.

2. In the same circle or equal circles, the chords subtended by equal central angles _________, and the arcs subtended by equal chords or equal arcs also ________; the central angles subtended by equal chords or equal arcs _________.

1. (4 points) It is known that the radius OA of ⊙O=5 cm and the chord CD=5 cm in the figure ⊙O, then the central angle subtended by the chord CD is ________.

2. (4 points) Which of the following statements is correct ()

A. If one side of an angle passes through the center of the circle, then the angle is the central angle

B. The value range of the central angle α is 0°＜α＜180°

C． The central angle is the angle whose vertex is at the center of the circle and the two sides of the angle are the rays where the two radii are located.

D． The central angle is the angle at the center of the circle

16. (10 points) In the figure, AB and DE are the diameters of ⊙O, C is a point on ⊙O, and AD�=CE�, what is the relationship between BE and the size of CE? Why?

BE=CE. Proof: Connect OC.∵AD�=CE�,

∴∠AOD=∠COE, and ∠AOD=∠BOE,

∴∠BOE=∠COE,

∴BE�=CE�,

∴BE=CE.

17． (12 points) As shown in the figure, in ⊙O, the radius OA⊥OB, C, and D are two trisection points of AB�, and the chords AB intersect OC and OD at points E and F respectively. Verify: AE=BF=CD.

(Tip: Connect AC, BD, proband: AC=CD=BD)

Connect AC, BD.∵C and D are the three bisecting points of AB�, ∴AC�=CD�=DB�, ∴∠AOC=∠COD=∠DOB, ∴AC=CD=BD.∵OA⊥OB, ∴∠AOB=90°, ∴∠AOC=30°. ∵OA=OC, ∴∠OAC=∠ACO=75°. And ∵OA=OB, ∴∠OAB=45°. ∵∠AEC=∠EAO＋∠AOC =45°+30°=75°, ∴∠AEC=∠ACE=75°, ∴AE=AC. In the same way, it can be proved that BF=BD, ∴AE=BF=CD

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"Central Angle and Circumferential Angle" PPT courseware 3:

"Central Angle and Circumferential Angle" PPT Courseware 3 1. The angle of a circle subtended by the same arc is ________. 2. A quadrilateral with four vertices on the same circle is called __________. This circle is called _____________. The circle inscribes the opposite angle of the quadrilateral _______. 1. (3 points) Next...

"Central Angle and Circumferential Angle" PPT courseware 2:

"Central Angle and Circumferential Angle" PPT Courseware 2 1. The angle where the vertex is on the circle and both sides are _________ with the circle is called _________. 2. The circumferential angle subtended by an arc on a circle is equal to the ________ of the central angle subtended by it. 3． The angle of the circle subtended by the semicircle (or diameter) is______..

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Update Time: 2024-07-10

This template belongs to Mathematics courseware Hebei Education Edition Ninth Grade Mathematics Volume 1 industry PPT template

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