Perhatikan gambar lingkaran dengan pusat O! Jika besar sudut AOD=80, besar sudut ACB=.... C D O A...

Summary

This educational video explains the relationship between central and inscribed angles in a circle. It starts by detailing the given central angle of 80° and demonstrates how to calculate the corresponding inscribed angle, ACB. By showing that the central angle AOB is supplementary to AOD, the video teaches that the inscribed angle ACB is half the measure of the central angle subtending the same arc. In this case, the inscribed angle ACB is calculated to be 50°. The lesson is concluded with the correct answer being option B.

Takeaways

• 😀 The script discusses the relationship between central angles and inscribed angles in a circle.
• 😀 The focus is on calculating the inscribed angle ACB using the known central angle AOD.
• 😀 The angle AOD is given as 80 degrees, and the task is to find the value of angle ACB.
• 😀 The inscribed angle ACB is formed by two chords AC and BC that intersect on the circumference of the circle.
• 😀 The inscribed angle (ACB) is described as a 'circumferential angle' in the script.
• 😀 The relationship between a central angle and the corresponding inscribed angle is explained: the inscribed angle is half the central angle.
• 😀 Angle ACB faces the arc AB, and the central angle AOB subtends the same arc.
• 😀 The central angle AOB is described as supplementary to the central angle AOD, meaning their sum is 180 degrees.
• 😀 Since AOD is 80 degrees, the central angle AOB is calculated as 180 - 80 = 100 degrees.
• 😀 The inscribed angle ACB is then calculated as half of the central angle AOB, resulting in 50 degrees.
• 😀 The correct answer for the value of angle ACB is 50 degrees, as calculated using the formula for inscribed angles.

Q & A

What is the main topic discussed in the transcript?

The main topic discussed is the relationship between central angles and inscribed angles in a circle, and how to calculate the value of an inscribed angle based on the central angle.

What is the value of angle AOD in the transcript?

The value of angle AOD is 80 degrees, as mentioned in the transcript.

What is the goal of the problem presented in the transcript?

The goal is to determine the size of the inscribed angle ACB, based on the given central angle AOD, which is 80 degrees.

What is an inscribed angle, and how is it related to a central angle?

An inscribed angle is formed by two chords of a circle that intersect at a point on the circumference. It is related to a central angle because the inscribed angle is always half the size of the central angle that subtends the same arc.

How does the central angle AOB relate to the inscribed angle ACB?

The central angle AOB is associated with the same arc as the inscribed angle ACB. The size of the inscribed angle ACB is half of the size of the central angle AOB.

What is the size of angle AOB, and how is it calculated?

The size of angle AOB is calculated by subtracting the value of angle AOD from 180 degrees, since angle AOD and angle AOB form a straight line. Therefore, angle AOB = 180 degrees - 80 degrees = 100 degrees.

How do we calculate the value of the inscribed angle ACB?

The value of the inscribed angle ACB is half the size of the central angle AOB. Since angle AOB is 100 degrees, the inscribed angle ACB is 100 degrees / 2 = 50 degrees.

Why is the inscribed angle ACB considered half the size of the central angle AOB?

This is a fundamental property of circles. The inscribed angle subtended by a given arc is always half the measure of the central angle subtended by the same arc.

Which answer choice corresponds to the correct size of angle ACB?

The correct size of angle ACB is 50 degrees, which corresponds to answer choice B.

What is the relationship between angles AOD, AOB, and ACB in this problem?

In this problem, angle AOD is the central angle, and angle ACB is the inscribed angle subtended by the same arc. Angle AOB is related to AOD as a supplementary angle, and ACB is half of AOB.