"Central Angle and Circumferential Angle" PPT Courseware 2

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"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 circumferential angle subtended by a semicircle (or diameter) is ________; the chord subtended by a 90° circumferential angle is ________.

1. (3 points) As shown in the figure, ∠APB is the angle of the circle ()

2. (4 points) As shown in the figure, the angle of the circle has ____________________.

3． (3 points) As shown in the figure, in ⊙O, ∠BOD=30°, OD∥AB, AD, OB intersect at point C, then the degree of ∠BCD is ()

A. 15°B. 30°C. 45° D. 60°

4． (3 points) (2013·Chengdu) In the figure, points A, B, and C are on ⊙O, ∠A=50°, then the degree of ∠BOC is ()

A. 40°B. 50°C. 80° D. 100°

5. (3 points) As shown in the figure, in ⊙O, the chord AB∥CD, if ∠ABC=40°, then ∠BOD=()

A. 20°B． 40°C. 50° D. 80°

6. (3 points) As shown in the figure, four small squares with side length 1 form a large square. A, B, and O are the vertices of the small square. The radius of ⊙O is 1. P is a point above ⊙O and is located on the upper right. Within a small square, then ∠APB is equal to ()

A. 30°B. 45°C. 60° D. 90°

15． (12 points) As shown in the figure, ⊙O is the circumcircle of △ABC, AB is the diameter of ⊙O, D is the point above ⊙O, OD⊥AC, and the vertical foot is E, connecting BD.

(1) Prove: BD bisects ∠ABC;

(2) When ∠ODB=30°, verify: BC=OD.

16. (12 points) In the figure, AB is the diameter of ⊙O, AB=AC, BC intersects ⊙O at point D, AC intersects ⊙O at point E, ∠BAC=45°.

(1) Find the degree of ∠EBC;

(2) Verify: BD=CD.

17． (14 points) As shown in Figure ①, it is known that △ABC is an equilateral triangle, ⊙O with BC as the diameter intersects AB, and AC is at points D and E.

(1) Verify: △DOE is an equilateral triangle;

(2) As shown in Figure ②, if ∠A=60° and AB≠AC, does the result of (1) hold? If it is true, please provide proof. If it is not true, please explain the reason.

(1)∵△ABC is an equilateral triangle, ∴∠B=∠C=60°. In △BOD and △COE, BO=OD, OC=OE, ∴△BOD and △OCE are all equilateral triangles. ∴∠BOD=∠EOC=60°, ∴∠DOE=60°. And ∵OD=OE, ∴△DOE is an equilateral triangle

(2) is established, prove: connect BE, BE⊥AC, and ∵∠A=60°, ∴∠ABE=30°, ∴∠DOE=60°. Also ∵OD=OE, ∴△DOE is an equilateral triangle

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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:

"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..

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Update Time: 2024-07-08

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

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