Soal Layang-Layang Garis Singgung | Garis Singgung Lingkaran 11 SMA KMerdeka

Summary

The script explains a geometry problem involving a circle, a tangent from a point outside the circle, and the calculation of related quantities such as the length of the tangent, the area of a triangle, the area of a kite, and the length of a chord. The steps include using the Pythagorean theorem to calculate the length of the tangent, finding the area of the triangle, calculating the kite's area, and determining the chord's length. The problem showcases how to apply geometry concepts like right triangles and area formulas in a real-world context.

Takeaways

• 😀 The problem involves a circle with a tangent drawn from a point outside the circle to the point of tangency.
• 😀 The length of the radius of the circle (OA) is given as 9 cm.
• 😀 The length of the distance from the point outside the circle (P) to the center of the circle (O) is 15 cm.
• 😀 The length of the tangent (AP) can be found using the Pythagorean theorem, resulting in 12 cm.
• 😀 The triangle formed by the radius (OA), the distance (OP), and the tangent (AP) is a right triangle.
• 😀 The area of triangle OAP is calculated using the formula for the area of a triangle, yielding 54 cm².
• 😀 The area of the kite (OAPB) is double the area of triangle OAP, which equals 108 cm².
• 😀 The kite’s diagonals are used to calculate its area, and diagonal OP is known to be 15 cm.
• 😀 The length of the chord AB (one of the diagonals of the kite) is calculated using the area formula for a kite, resulting in 14.4 cm.
• 😀 The script involves applying basic geometric principles, such as the Pythagorean theorem, triangle area, and properties of tangents and kites.

Q & A

What is the main topic of the video?

The main topic of the video is solving a mathematical problem involving tangents to a circle, the Pythagorean theorem, and calculating areas of geometric shapes such as a triangle and a kite.

What is the relationship between the points P, A, and B in the script?

In the script, points A and B are the points of tangency where two tangents from point P meet the circle. These tangents are of equal length, meaning PA = PB.

How is the length of AP determined in the script?

The length of AP is determined using the Pythagorean theorem. Given that triangle OAP is a right triangle, we calculate AP as the square root of (OP^2 - OA^2). The result is 12 cm.

What geometric principle is used to calculate the length of AP?

The Pythagorean theorem is used to calculate the length of AP, as triangle OAP is a right triangle with the right angle at point A.

What formula is used to find the area of triangle OAP?

The area of triangle OAP is calculated using the formula for the area of a triangle: (1/2) * base * height. Here, the base is OA (9 cm), and the height is AP (12 cm).

What is the area of triangle OAP?

The area of triangle OAP is 54 cm², calculated as (1/2) * 9 * 12.

How is the area of the kite OAPB calculated?

The area of the kite OAPB is twice the area of triangle OAP because the kite is made up of two congruent triangles. Therefore, the area of the kite is 108 cm².

What is the formula for calculating the area of a kite?

The area of a kite is calculated using the formula: (1/2) * diagonal 1 * diagonal 2, where diagonal 1 is OP and diagonal 2 is AB.

How do we find the length of chord AB in the script?

The length of chord AB is calculated using the area of the kite. By rearranging the area formula for the kite, we solve for AB and find it to be 14.4 cm.

Why is chord AB referred to as the 'tali busur' (chord of the arc)?

Chord AB is referred to as the 'tali busur' because it faces the arc of the circle, and it is the line connecting the two points of tangency (A and B).