(Part 2) GARIS SINGGUNG LINGKARAN MATEMATIKA SMA KELAS 11 KURIKULUM MERDEKA #kurikulummerdeka
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Exploring Tangent Lines on a Circle
- A tangent line on a circle is where a train wheel or a line touches the circle at exactly one point, known as the tangent point.
- In the case of a ship navigator calculating the distance to ports on the horizon, the blue line represents the navigator's view of the sea and acts as a tangent line.
- Tangent lines must intersect the circle at only one tangent point.
- The angle formed by the tangent line and the radius of the circle at the point of tangency is always 90 degrees, making the tangent line perpendicular to the radius.
- The angle between the tangent line and the radius remains 90 degrees even if the tangent point is different.
Understanding Tangent Lines to Circles
- A tangent line to a circle intersects the circle at only one point.
- The angle formed between the tangent line and the radius of the circle is always 90°, as they are perpendicular to each other.
- When investigating different images of tangent lines, it is important to remember that the tangent line must be perpendicular to the radius of the circle.
- The angle formed by a tangent line and the radius at the point of tangency is always 90 degrees.
- A line that does not form a right angle with the radius of the circle is not a tangent line.
- A tangent line intersects the circle at only one point, while a non-tangent line can intersect the circle at multiple points.
- The condition for a tangent line is that it intersects the circle at one point and forms a 90° angle with the radius.
Understanding Tangent Lines and Congruent Triangles
- Tangent lines are lines that intersect a circle at exactly one point, called the tangent point.
- The angle formed between a tangent line and the radius of the circle is always 90°.
- Triangle ABP and triangle ACP are congruent because they have the same shape and size.
- The length of PB is equal to the length of PC because they are both tangent lines.
- The angle APB and the angle APC are both 45°.
- From a point outside the circle, two tangent lines can be drawn of equal length.
- In navigation, knowing the radius of the Earth and the height of the ship, the distance between the ship and a port visible on the horizon can be determined.
Calculation of Distance (D) using the Pythagorean Theorem
- The Pythagorean theorem is applied to a right-angled triangle formed by points C, H, and O.
- The distance between the navigator and the port is represented by D.
- In the triangle CHO, the squared hypotenuse (HO²) is equal to the sum of the squares of the other two sides (HC² and OC²).
- D² is equal to HO², which is equal to (R + h)² - r².
Understanding Tangent Lines on a Circle and their Applications
- Tangent lines touch a circle at exactly one point, known as the tangent point.
- The angle between a tangent line and the radius of the circle at the point of tangency is always 90 degrees.
- Tangent lines must intersect the circle at only one tangent point.
- Tangent lines are perpendicular to the radius of the circle.
- A non-tangent line does not form a right angle with the radius of the circle.
- Triangle ABP and triangle ACP are congruent because they have the same shape and size, and the length of PB is equal to the length of PC because they are both tangent lines.
- Two tangent lines of equal length can be drawn from a point outside the circle.
- In navigation, the distance between a ship and a visible port on the horizon can be determined using tangent lines and the Pythagorean theorem.