Circles with Equal Radii: Definition
Circles that share the same radius length are referred to by a specific geometric term.
Understanding Circle Terminology
In geometry, circles are compared based on their properties, primarily their radius and diameter.
- Equal Radii: When two or more circles have radii of the same length, they are identical in size.
- Congruent Circles: This is the term used for circles that have the same size and shape. Having the same radius is the defining characteristic of congruent circles.
- Similar Circles: Circles are always similar to each other because they have the same shape, regardless of their size (radius).
Identifying Congruent Circles
The defining feature of congruent circles is that their radii are equal. If two circles have radii \(r_1\) and \(r_2\), they are congruent if and only if \(r_1 = r_2\).
Options Analysis:
- Chord of the circle: A line segment connecting two points on the circle's circumference. This is a part of a single circle, not a comparison between circles.
- Similar circles: All circles are similar because they have the same shape. Similarity does not require equal radii.
- Congruent circles: This term precisely describes circles with equal radii, meaning they are identical in size and shape.
- Center of the circle: The central point around which the circle is drawn. This is a property of a single circle.
Therefore, circles having equal radii are called congruent circles.
Important Questions from Circles
If 3x + y - 5 = 0 is the equation of a chord of the circle x2 + y2 - 25 = 0, then what are the coordinates of the mid-point of the chord ?
What is the area of minor segment ?
What is the area of major segment ?
A straight line x = y + 2 touches the circle 4(x 2+ y 2) = r 2. The value of r is
If the centre of the circle passing through the origin is (3, 4), then the intercepts cut off by the circle on x-axis and y-axis respectively are
