Sudut pusat dan sudut keliling lingkaran

Summary

In this educational video, the presenter explains the concepts of central and circumscribed angles in a circle, demonstrating their definitions, properties, and relationships. A central angle has its vertex at the center of the circle, while a circumscribed angle's vertex lies on the circumference. The video highlights the key formula that the central angle is twice the size of the circumscribed angle. Through clear step-by-step examples, viewers learn how to calculate these angles in various scenarios, enhancing their understanding of geometric principles involving circles.

Takeaways

• 😀 The video explains the concepts of 'central angle' and 'inscribed angle' in circles.
• 😀 The central angle is formed by two radii with the vertex at the center of the circle.
• 😀 An inscribed angle is formed by two chords with the vertex on the circumference of the circle.
• 😀 The central angle and inscribed angle that subtend the same arc are related by a specific rule: the central angle is twice the inscribed angle.
• 😀 The formula for the central angle is twice the measure of the inscribed angle when they subtend the same arc.
• 😀 Example problem: To find the central angle, multiply the inscribed angle by 2.
• 😀 Example problem: To find the inscribed angle, divide the central angle by 2.
• 😀 The angles of a circle follow specific geometric properties and rules based on their position relative to the circle’s center and circumference.
• 😀 The video presents a few example problems to demonstrate how to apply the central and inscribed angle rules.
• 😀 The tutorial emphasizes the importance of understanding the relationship between the central and inscribed angles for accurate problem-solving.

Q & A

What is a central angle in a circle?

A central angle is an angle whose vertex is at the center of the circle, and whose sides are formed by two radii of the circle.

What defines an inscribed angle in a circle?

An inscribed angle is an angle whose vertex lies on the circumference of the circle, and whose sides are formed by two chords of the circle.

What is the relationship between central and inscribed angles?

The central angle is always twice the measure of the inscribed angle that subtends the same arc of the circle. Conversely, the inscribed angle is half the measure of the central angle.

How do you calculate the central angle from the inscribed angle?

To find the central angle, multiply the inscribed angle by 2. The formula is: Central Angle = 2 × Inscribed Angle.

How do you calculate the inscribed angle from the central angle?

To find the inscribed angle, divide the central angle by 2. The formula is: Inscribed Angle = 1/2 × Central Angle.

In the provided examples, what was the inscribed angle when the central angle was 60°?

When the central angle was 60°, the corresponding inscribed angle was 30°, calculated by dividing the central angle by 2.

In the second example, if the inscribed angle is 35°, what is the central angle?

If the inscribed angle is 35°, the central angle is 70°, calculated by multiplying the inscribed angle by 2.

What happens when the central and inscribed angles share the same arc in the circle?

When the central and inscribed angles share the same arc, the central angle will always be twice as large as the inscribed angle.

Can you provide an example where two angles subtend the same arc but are different types?

In the example with angles ADB and ACB, both angles subtend the same arc AB. The angle ADB is a central angle, and the angle ACB is an inscribed angle. The central angle ADB is 80°, while the inscribed angle ACB is 40°.

What should be noted when applying the formulas for central and inscribed angles?

The formulas for central and inscribed angles only apply when the angles share the same arc of the circle. If the angles are not formed by the same arc, these relationships do not hold.