Tali Busur Lingkaran - Matematika SMA Kelas XI Kurikulum Merdeka

BSMath Channel

9 Oct 202307:10

Summary

TLDRIn this educational video, the concept of chords in circles is explored, particularly focusing on the definition of a chord (tali busur) and how to calculate its length using the Pythagorean theorem. Viewers are guided through a specific problem involving a circle with a given radius and apothem, illustrating the process of visualizing the geometry and applying mathematical principles to derive the length of the chord. The video encourages viewers to practice with additional exercises, reinforcing their understanding of this fundamental geometric concept.

Takeaways

😀 The discussion focuses on the concept of a chord in a circle, defined as a line segment connecting two points on the circumference.
📏 A chord is represented by the line segment connecting points K and L on circle P.
🔍 The center of the circle is denoted as point P, and the chord length is explored in the context of a problem involving triangle properties.
📐 The problem includes an apothem (line segment from the center to the midpoint of the chord) and a radius of the circle.
📝 The apothem OR is given as 8 cm, while the radius OP is 10 cm.
🔺 A right triangle is formed with the apothem and the radius, which allows for the application of the Pythagorean theorem to find the length of the chord.
⚖️ The lengths of the sides of the triangle are used to calculate the length of the chord PQ using the formula derived from the Pythagorean theorem.
✏️ The calculation shows that the length of segment RQ, which is half of PQ, is 6 cm.
📏 Consequently, the total length of the chord PQ is determined to be 12 cm.
💡 The method involves identifying relevant segments and using geometric principles to solve problems related to circles.

Q & A

What is a chord in a circle?
-A chord is a line segment that connects two points on the circumference of a circle.
How is the apothem related to a chord?
-The apothem is the line that connects the center of the circle to the midpoint of the chord.
In the example given, what are the lengths of the apothem and the radius?
-The length of the apothem (OR) is 8 cm, and the length of the radius (OQ) is 10 cm.
What is the goal of the problem discussed in the video?
-The goal is to find the length of the chord PQ in the circle.
How do we find the length of the chord using the Pythagorean theorem?
-We can use the Pythagorean theorem by identifying the lengths of the sides of the right triangle formed and calculating the length of the chord based on these lengths.
What is the relationship between the chord PQ and the segment RQ?
-RQ is half the length of the chord PQ, as R is the midpoint of PQ.
How is the length of RQ calculated in the example?
-RQ is calculated using the Pythagorean theorem: RQ = √(OQ² - OR²), which results in RQ = 6 cm.
What is the final length of the chord PQ in the example?
-The final length of the chord PQ is 12 cm, calculated as PQ = 2 * RQ.
What method is recommended for solving problems related to chords in a circle?
-The recommended method is to draw auxiliary lines to form a right triangle and then apply the Pythagorean theorem.
What should viewers do at the end of the video regarding practice problems?
-Viewers are encouraged to solve the practice problems provided at the end of the video and share their answers in the comments.