What type of circles are present in the figure?
– Common Circles
– Tangent Circles
– Congruent Circles
– Concentric Circles
Figure 1
The question aims to find what to call two circles that are in the same plane and have the same center point.
The question depends on the circle geometry concerning the similarity between circles. The circles can be co-planar, congruent, and concentric. The two circles can be called co-planar circles if they lie on the same 2D plane. The two circles will be called congruent circles, meaning equal circles, if their radii are equal. When the center points of two congruent circles are joined at a common point, both circles should have the same boundary by definition. The two circles are called concentric circles if they have the same center point regardless of their radii length.
The following figure shows different circles.
Figure 2
In Figure 1, circles A and B are shown. Both circles have equal radii, so they are called congruent circles. The circles have different center points but have same radii.
Expert Answer
Figure 1 shows a diagram of different circles on the same 2D plane. We need to choose one option from the given choices that represents the circles in the figure. Let us evaluate the given options to check which option is correct.
a) Common Circles:
This term is not a mathematically defined term. Common circles can be anything relating to the same radius or the same tangent line passing through a circle. It could also point toward two circles having a common area.
b) Tangent Circles:
In geometry, tangent is a line that passes through the circle from only one point and it is perpendicular to the radius from that point. Tangent circle is not a valid term in the mathematics of geometry. It is made up and here it is only to confuse the student.
c) Congruent Circles:
The congruent circles are two circles having the same length or value for the radius. It is also important to note here that both circles need not to be co-planar to be congruent to each other. This means that both circles are same. The circumference of both circles will also be same as the circumference of the circle depends on the radius of the circle. The circumference of the circle is given as:
\[ C = 2 \pi r \]
d) Concentric Circles:
Two or more circles having the same center point. As we can observe from the given figure that all the circles have a common center point. Thus, the circles given in the figure are concentric circles. It is important to note here is that the concentric circles must also be co-planar circles as well.
Numerical Result
The circles given in the figure are concentric circles.
Example
What type of circles are present in the figure given below?
Figure 3
Observing from the graphs, we can see that both circles have the same radius. We can clearly observe that both circles have radii equal to 3 units. This means that these circles given in the graph are congruent circles.