Garis Singgung Lingkaran(1) - Definisi, Panjang Garis Singgung | Matematika Kelas VIII SMP MTs

Summary

This educational video explains the concept of tangent lines to circles, starting with basic definitions and moving into calculations. It demonstrates how a tangent line touches a circle at exactly one point and is perpendicular to the radius at that point. The video covers calculating the length of tangent lines using the Pythagorean theorem, with examples that explore finding the tangent's length, the area of the formed triangle, and the radius of the circle. The video provides a clear and practical understanding of these geometric concepts, making it valuable for students learning about tangents and circle theorems.

Takeaways

• 😀 Tangents to a circle touch the circle at exactly one point, known as the point of tangency.
• 😀 There can only be one tangent drawn from a point on the circle, but from an external point, two tangents can be drawn.
• 😀 The tangent line is always perpendicular to the radius of the circle at the point of tangency.
• 😀 In geometric problems, the Pythagorean theorem is used to calculate the length of tangents drawn from an external point.
• 😀 The formula for calculating the length of a tangent (AB) from an external point is derived using the Pythagorean theorem.
• 😀 The tangent lengths from a single external point to a circle are always equal in length.
• 😀 Example problems help in understanding how to apply the Pythagorean theorem to find tangent lengths and triangle areas.
• 😀 The radius of the circle and the distance from the external point to the center are key elements when calculating tangent lengths.
• 😀 For right-angled triangles formed by a radius and a tangent, the area of the triangle can be calculated using the formula: Area = 1/2 × base × height.
• 😀 By applying the Pythagorean theorem in problems, both tangent lengths and areas of triangles can be solved effectively.

Q & A

What is a tangent line to a circle?

A tangent line to a circle is a line that touches the circle at exactly one point. This point is called the point of tangency, and the tangent line is always perpendicular to the radius of the circle at the point of tangency.

How many tangent lines can pass through a single point on the circle?

Only one tangent line can pass through a single point on the circle.

What happens when a point is located outside the circle?

When a point is located outside the circle, two tangent lines can be drawn from that point to the circle, each touching the circle at different points.

What is the relationship between the tangent line and the radius of the circle?

The tangent line is always perpendicular to the radius that connects the center of the circle to the point of tangency.

How do we calculate the length of a tangent line from a point outside the circle?

To calculate the length of a tangent line, we can use the Pythagorean Theorem. In a right triangle formed by the radius, the tangent line, and the distance from the circle's center to the external point, we apply the formula: tangent length = √(distance from center to external point² - radius²).

What does the Pythagorean Theorem state?

The Pythagorean Theorem states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. Mathematically: c² = a² + b².

What is the formula used to find the length of the tangent line in the video?

The formula to find the length of the tangent line is: tangent length = √(OB² - r²), where OB is the distance from the external point to the center of the circle, and r is the radius of the circle.

How can we find the area of a triangle formed by the radius and the tangent line?

The area of the triangle can be found using the formula for the area of a right triangle: Area = 1/2 × base × height, where the base is the radius and the height is the length of the tangent line.

What is the significance of the Pythagorean Theorem in this context?

The Pythagorean Theorem is crucial because it allows us to calculate the length of the tangent line from a point outside the circle, which is essential for solving geometry problems related to circles and tangents.

How do you solve for the radius if the length of the tangent and the distance from the external point to the center are given?

To solve for the radius, use the Pythagorean Theorem: r = √(OB² - tangent length²), where OB is the distance from the external point to the center, and the tangent length is the length of the tangent line.