# Worksheet and Formula list on Chord, Arc and Sector of a Circle

### On this page, find the formulae list for Chord, Arc, Sector and Circle. We also have a worksheet with practice examples with explanation for solving on the topic

**Chord: **A chord is a line segment whose endpoints lie on the circumference of a circle.

Please Note: A Diameter is the longest Chord of the cirlce.

**Arc:** An arc is a portion of the circumference of a circle. It can be measured in degrees or radians. Eg. arc AXB

**Sector: **A sector is a portion of a circle bounded by two radii and the arc between them. Eg. OAXB or Sector OAB

**Easy Level Worksheet on Chord, Arc, and Sector of a Circle**

1. **Area and Perimeter of Circle:** A circle has a radius of 7 cm. Calculate its area and perimeter (circumference).

2. **Area of a Sector:** Find the area of a sector with a central angle of 60 degrees in a circle of radius 10 cm.

3. **Arc Length:** Calculate the length of an arc subtended by a central angle of 45 degrees in a circle with a radius of 8 cm.

4. **Chord Length:** In a circle with a radius of 12 cm, a chord is 16 cm long. Find the distance from the center of the circle to the chord.

5. **Perimeter of a Sector:** A sector of a circle has a radius of 9 cm and a central angle of 90 degrees. Calculate the perimeter of the sector.

6. **Area of a Segment:** A circle has a radius of 6 cm and a central angle of 120 degrees. Calculate the area of the segment (the area of the sector minus the area of the triangle).

7. **Area of Multiple Sectors:** A circle is divided into 4 equal sectors. If the radius of the circle is 5 cm, calculate the area of one sector.

8. **Finding Radius from Sector Area:** The area of a sector of a circle is 50 square cm, and the central angle is 72 degrees. Find the radius of the circle.

9. **Length of a Chord Using Angle:** A chord in a circle subtends a central angle of 60 degrees, and the radius of the circle is 10 cm. Calculate the length of the chord.

10. **Arc and Sector Angle Relationship:** A circle has a radius of 15 cm. If an arc is 20 cm long, find the measure of the central angle subtended by the arc in degrees.

**Medium Level Worksheet on Chord, Arc, and Sector of a Circle**

### Chord

Imagine you have a pizza. A chord is like the string you use to cut straight across the pizza, making a direct path from one edge to another. It doesn't necessarily pass through the center; it just connects two points on the crust.

**Why it matters: **It's like knowing shortcuts in life. Understanding chords helps you find the shortest path between two points on a circle, which is useful in various real-life situations.

### Arc

Now, think about the crust of that pizza slice. The arc is the curved part of the crust. It's not a straight line but a part of the circle's edge.

**Why it matters: **It's similar to following a curved path, like walking around the edge of a park instead of cutting straight through. Understanding arcs helps you grasp the idea of distance along a curve, which is important in many areas, like designing roads or tracks.

### Sector

A sector is like a slice of pizza. It's the part of the pizza that's between two cuts and includes the crust (arc) and the straight lines (radii) from the center to the crust.

**Why it matters: **Imagine you're sharing a pizza with friends. Knowing about sectors helps you understand how to divide things fairly and equally. It also helps you in situations where you need to measure and understand parts of a whole, like dividing up land or space.

### Importance for School Students

**Foundational Knowledge**: These concepts are like learning the ABCs of geometry. They are the building blocks for more complex ideas you'll encounter later.**Real-Life Problem Solving**: Just like you'd use a map to find your way, understanding these concepts helps you solve everyday problems, whether you're baking, planning a garden, or designing something.**Advanced Learning**: Think of these concepts as stepping stones. Mastering them prepares you for more advanced subjects in high school and beyond, like physics, engineering, and architecture.**Analytical Skills**: Working with these shapes and figures sharpens your mind. Itâ€™s like mental exercise that makes you better at thinking logically and solving problems creatively.

By understanding chords, arcs, and sectors, you're not just learning about circles. You're learning how to think about space, shapes, and measurements in a way that applies to many parts of life. Whether you're cooking, playing sports, or planning a project, these concepts help you see the world in a more structured and insightful way.