Which Circles Are Congruent?
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- In the plane, all circles of the same radius are congruent to one another. In this case, radius AB is of the same length as the radius DC.
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- Here is a great video on congruent circles and their properties!
By Liza Sulkin
- Geometrically, congruence is a property of at least two shapes relative to each other. If two shapes are congruent, then they share the exact same properties. Furthermore, congr…
By Liza Sulkin
- We said earlier that congruent circles are exactly identical. This property has some interesting consequences. Since congruent circles can be defined by their congruent radii, p…
By Liza Sulkin
Problems 20
- Circle A has center at the origin and radius x. It is rotated 90∘90^{\circ}90∘ clockwise. Circle B has center at the origin and radius y. It is rotated 90∘90^{\circ}90∘ counterc…
- A red, a green, and a blue car race around a circular track of radius n. In the time it takes the red car to complete a lap, the green car completes two laps. The blue car, mean…
- Circle A has center at (1, 3) and radius 2. Circle B has center at (1, 3) and radius 4. Circle C has center at (2, -7) and radius 2. Which (if any) of these circles are congruent?
- Circle A has center at (4, 4) and radius 9. Circle B has center at (4, 4) and radius 5. Circle C has center at (4, 4) and radius π\piπ. Which (if any) of these circles are congr…
- Two congruent circles are inscribed within a rectangle. What is the ratio of the area of both circles to that of the rectangle?
- Which of the following circles are congruent to the circle above?
- Which of the following circles is congruent to ∘BC\circ{BC}∘BC? (Assume they are all circles).
- Consider the Via Cadememi\textit{Via Cadememi}Via Cadememi in Italy. Given the fact that the two circles are congruent, find the radius of each circle.
- Consider the O House\textit{O House}O House in Switzerland. Find the radius of one of the circles given they are all congruent.
- Consider the stoplight above. City officials want to covert it to a yellow slow warning light. Because of this, city officials need to cover up the green and red lights with an …
- Suppose circle A has radius X and circle B has radius Y. When are these two circles similar?
- Suppose circle A has radius X and circle B has radius Y. When are these two circles congruent?
- Similar polygons are those with proportional corresponding sides. What analogous proportional structures do similar circles have?
- Congruent polygons are those with congruent corresponding sides. What analogous congruent structures do congruent circles have?
- Consider spheres. In some sense, spheres can be considered 3D circles because they are the set of points that a constant distance away from a point in space. Suppose Sphere A ha…
- Suppose you have different polygons inscribed in congruent circles. Which of the following polygons would take up the largest area within the circle?
- Which of the following are congruent in congruent circles?
- Suppose you're looking at the buttons on a shirt. Which of the following are results of properties of congruent circles?
- The fractal above is constructed by taking a large circle, surrounding it by four smaller circles, and then iteratively building three relatively small, circles from the four sm…
- The planet Saturn has distinctive rings orbiting its body. These rings are mostly composed of ice and elements that travel in circular paths around the planet; their proximity t…