Final answer:
Based on the true statements shown, it can be concluded that if a line segment is a diameter, then it is the longest chord in a circle. Line segment AB is a diameter, therefore it is the longest chord in the circle.
Step-by-step explanation:
A circle is a shape in which all points on the boundary are equidistant from the center point. A chord is a line segment that connects two points on the circle's boundary. A diameter is a chord that passes through the center of the circle. It is also the longest chord in the circle, as it crosses the circle's center point and touches the circle's boundary at two points, making it longer than any other chord.
To understand this concept mathematically, let us consider a circle with a diameter of length d. According to the Pythagorean theorem, the length of the diameter can be calculated using the formula d=√(r^2+r^2), where r is the radius of the circle. Therefore, the length of the diameter is equal to twice the radius of the circle.
Now, let us assume that line segment AB is a chord in the circle and it is not a diameter. This means that it does not pass through the center of the circle. So, the length of AB can be calculated using the formula AB=√(r^2+x^2), where x is the distance from the center of the circle to the midpoint of AB. As x is always less than r, the length of AB will always be shorter than the length of the diameter.
Hence, it can be concluded that if a line segment is a diameter, it is the longest chord in the circle. And since line segment AB is a diameter, it is the longest chord in the circle. This is because it crosses the circle's center point and touches the circle's boundary at two points, making it longer than any other chord.
In simpler terms, the diameter of a circle is like the backbone that runs through the center and supports the circle, making it the longest chord. And since line segment AB is a diameter, it fulfills the conditions of being the longest chord in the circle.
In conclusion, based on the given statements, it can be concluded that if a line segment is a diameter, then it is the longest chord in a circle. Line segment AB is a diameter, therefore it is the longest chord in the circle. This can be understood both visually and mathematically, making it a valid and accurate conclusion.