Test: Circle - Class 9 MCQ

If a line from the center of the circle bisects a chord, it divides the chord into two equal segments. This property is essential in proving various theorems related to chords and their relationships within circles.

The angle subtended by a chord at the center of a circle is referred to as a central angle. This angle is crucial for understanding the relationships between chords, arcs, and angles in a circle, particularly in theorems related to circle geometry.

Two circles are considered equal or congruent when their radii are equal. This property is essential when determining the relationships between different circles in geometry, such as in constructions and proofs.

An interior point of a circle is defined as a point where the distance from the center is less than the radius. Understanding these points is crucial in various geometric applications and proofs involving circles.

Theorem 26 asserts that one unique circle can be drawn through three non-collinear points. This theorem is significant in geometry, particularly in constructions and proofs involving triangles and polygons.

An inscribed circle touches all sides of a polygon, while a circumscribed circle passes through all vertices of the polygon. This distinction is vital in triangle geometry and other polygons, providing insight into their properties and relationships.

If two arcs are equal, it follows that the chords subtended by those arcs are also equal. This relationship is fundamental in circle geometry, providing insight into how arcs and chords interact.

The diameter of a circle is defined as a chord that passes through the center, making it the longest chord of the circle. It is also equal to twice the radius, which is a key relationship in circle geometry.

The term "locus" refers to the path traced by a point that maintains a constant distance from a fixed point, which is the center of the circle. This concept is fundamental in defining circles and understanding their geometric properties.

If the radius of a circle is doubled, the circumference also doubles, as the circumference is directly proportional to the radius. This relationship is captured by the formula C = 2πr, emphasizing the importance of understanding these fundamental properties.

Concentric circles are those that have the same center point but differ in radii. This concept is often used in various applications, such as in design and architecture, where multiple circular patterns are created around a central point.

A minor arc is defined as an arc that is less than a semicircle. This is crucial for understanding how to calculate and differentiate between different types of arcs in circular geometry.

A segment is defined as the area enclosed by a chord and the corresponding arc. There are minor segments and major segments based on whether the area is less or more than half of the circle, respectively, which is important in various applications in geometry.

The theorem states that equal chords in a circle are equidistant from the center. This means that if two chords have the same length, the perpendicular distances from the center to these chords will also be equal, which is a fundamental property used in circle theorems.

A circle is defined as a closed curve in which every point is equidistant from a fixed point known as the center. This fundamental property distinguishes circles from other geometric shapes and is pivotal in various geometric concepts and applications.

Theorem 22 states that a line drawn from the center of a circle that bisects a chord (which is not a diameter) will be perpendicular to that chord. This theorem is fundamental in proving various properties related to chords and their relationships within circles.

The circumference of a circle is calculated using the formula C = 2πr. For a radius of 7 cm, the circumference would be C = 2π(7) = 14π cm. This formula is fundamental in circle geometry and helps in various practical applications.

The angles subtended by equal arcs at the center of a circle are equal. This property is essential for understanding the relationships between arcs and angles in circle geometry.

An arc is defined as a portion of the circumference of a circle. Arcs can be classified as minor arcs, which are smaller than a semicircle, and major arcs, which are larger than a semicircle. This distinction is important in understanding the relationships between angles and arcs in circle geometry.

In a right triangle formed in this context, the radius is always the longest side, according to the Pythagorean theorem. This relationship is critical for solving problems related to circles and chords.