Adv.Math - Parts Of A Circle Homework

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The given options are different representations of the word "circle". The correct answer is "O" because it is a capital letter and commonly used to represent a circle in mathematical notations. The other options "o" and "0" are lowercase letter and number respectively, which are not commonly used to represent a circle. The option "circle o" is a phrase that describes a circle but is not a specific name for it.

The given options MN, mn, nm, and NM all represent the diameter of a circle. The diameter is a line segment that passes through the center of a circle and connects two points on its circumference. It is the longest chord in a circle and is always twice the length of the radius. In this case, the options provided represent different combinations of uppercase and lowercase letters, but they all refer to the same concept of a diameter.

The diameter of a circle is a line segment that passes through the center of the circle and has both endpoints on the circle. In the given options, only MN satisfies this condition. Therefore, MN is the correct answer for choosing the diameter in Circle O.

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The question asks for the radius that is NOT a radius of Circle O. MN is the only option that is not a radius of Circle O.

The statement "All chords are diameters" is false. A chord is a line segment that connects two points on the circumference of a circle, whereas a diameter is a chord that passes through the center of the circle. Therefore, while all diameters are chords, not all chords are diameters.

The statement "Some radii are chords" is false. A radius is a line segment that connects the center of a circle to any point on the circumference, while a chord is a line segment that connects any two points on the circumference. Since a radius is always shorter than or equal to the diameter, it cannot be a chord unless it coincides with the diameter, making it the longest chord in the circle. Therefore, not all radii are chords.

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The statement "All central angles are acute" is false. A central angle is an angle whose vertex is at the center of a circle and its sides pass through two points on the circumference. Central angles can have any measure, including acute, right, or obtuse angles. Therefore, not all central angles are acute.

All diameters are chords because a chord is a line segment that connects two points on a circle. A diameter is a special type of chord that passes through the center of the circle, dividing it into two equal halves. Therefore, every diameter can also be considered as a chord.

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The central angles of a circle are the angles formed by two radii with their vertex at the center of the circle. In this case, PON, MON, and MOP are all central angles because they are formed by radii of Circle O with their vertex at the center.