**What type of circles are present in the figure?**

**– Common Circles**

**– Tangent Circles**

**– Congruent Circles**

**– Concentric Circles**

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.

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?

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.**