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How do you show that all circles are similar?
Take any two circles, and slap some Cartesian Coordinates on them, such that the first is at the origin. Translate the second circle to the origin, then dilate it until the radii match. Thus the pair of circles is similar.
Do all circles have the same radius?
By definition, all radii of a circle are congruent, since all the points on a circle are the same distance from the center, and the radii of a circle have one endpoint on the circle and one at the center.
Are circles with the same radii similar?
Answer: Since a radius is a constant (an unchanging number), and any constant is only equal to another constant when they are equal, then all circles with the same radii (or values dependent on radii) must be congruent. A related geometric property is similarity. Similar shapes are proportional in every possible way.
Why do all radii of a circle have the same length?
By the definition of a circle, any two radii have the same length. Since a diameter consists of two radii joined at their endpoints, every diameter has length equal to twice the radius. Hence, all radii of a circle are equal.
What do all circles have in common?
While they have different colors and different radii, they are still similar. All circles are similar to each other. All points on the circumference of any circle are equi-distant from its center. Because the size of any circle is defined by its radius, we use the radii to determine its scale factor.
What are two circles with the same radius?
Concentric Circles: Two or more circles that have the same center, but different radii. Congruent Circles: Two or more circles with the same radius, but different centers.
Do all circles have the same shape?
All circles have the same shape i.e. they are round. But the size of a circle may vary. Thus circles are similar.
What is the same about the two circles?
Because a circle is defined by its center and radius, if two circles have the same center and radius then they are the same circle. This proves that in general, all circles are similar.
Who is the longest chord of the circle?
diameter
A chord that passes through the center of a circle is called a diameter and is the longest chord of that specific circle.
Is a radius the same length as a chord?
r is the radius of the circle. c is the angle subtended at the center by the chord. d is the perpendicular distance from the chord to the circle center….More Topics Related to Chord and Chord Length of Circles.
| Parts of a Circle | Properties of Circle |
|---|---|
| Circumference of a Circle | Radius Of A Circle |
Which pair of circles is congruent?
Two circles are congruent if they have the same size. The size can be measured as the radius, diameter or circumference. They can overlap.