Math is one of those subjects that daunts many students because of its never-ending formulas and theorems. So, if you also think “Who can do my math homework,” you are not alone. As several pupils think the same due to circles, a topic in math. So, this write-up will equip you with all the aspects you must know while working on it.

Basic Terminology Related to Circles

Listed below are the fundamental terms used concerning a circle. Have a look:

Segment

A segment is a region between one of the arcs of the circle and a chord. This region is a segment of the whole circle. In other words, when you divide something into parts, each one is called a segment. But, in a circle, a specific part that is cut by a chord is the segment.

The formula of a segment is: Area of a Segment in Radians A = (½) × r2(θ – Sin θ)

Tangent

Basically, a tangent is an intersecting line that touches the circle at the same point on the circumference. In addition, this does not enter a circle’s inner side. A tangent is perpendicular to the radius. There may be many tangents in a circle.

Formula of a tangent: Y=m x+c

Chord

The definition of a chord is a line segment that joins any two points in the circumference of the circle. Moreover, the diameter is the longest chord that passes through the center of a circle.

Formula of a Chord: Length of chord = 2√ (r2– d2)

Radius

A radius is a line that joins the center of a circle to its boundary. You should note that the length from any point to the radius will remain the same.

The formula for a radius is: r= c/2π

Arc

An arc, or the arc length, is the distance along the path of the circumference of any curve or circle. In other words, any distance along the curving path of the circumference of the circle is termed the arc.

The formula of an arc is: 2πr (θ/360)

Circumference

The circumference is the perimeter of the circle. In other words, it is the length of the circle’s boundary.

The formula for a circumference is: C= 2πr

Now you have an idea of the basic terminologies that you will come across in the circle’s chapter. Let us now equip you with the different theorems related to it.

Theorems and Applications

Here are some common theorems related to circles that you will be using in your math homework:

Theorem 1:

Equal chords subtend equal angles at the center of a particular circle.

Meaning:

The basic explanation of this theorem is that an angle in a circle is created by the two chords that meet at a point on the circumference.

How to Find Subtend Angles:

  • Use angle facts to find the angle that is missing.
  • Use the particular circle theorem to figure out the subtended angle.

Theorem 2:

Angles from the same chord in the same segment are equal.

Meaning:

If there are two triangles within a circle whose all three sides touch the circle and the triangle shares a side, then the third angle in both triangles will be equal. But these angles must be in the same segment to be equals.

How to Apply the Same Segment Theorem:

  • Find the main parts of the circle for the theorem.
  • Use the same segment to find one of the missing angles.

Theorem 3:

Opposite angles in a cyclic quadrilateral sum to 180°.

Meaning:

This theorem states that the sum of the opposite angles in a cyclic quadrilateral is 180 degrees. A cyclic quadrilateral is a four-sided shape whose all the corners touch the particular circle.

So, these are some commonly used theorems of a circle that you will be using while working on your math task. Although using them appropriately is challenging, it can become smoother with professional math homework help online.

Tips to Have Your Hands on Circles Easily

Here are some of the tips that will make you have your hands on circles easily:

Do Not Practice One Type of Question

One of the biggest mistakes students make is they stick to only a particular type of question for practice. It is a mistake because, in the exams, there will be several types of questions to solve. So, they must prepare for numerous problems to pass their test. Therefore, you must attempt different kinds of issues while practicing circle theorems.

Never Overlook the Basics

Solving problems using circle theorems is not challenging if you have your hands on the fundamentals. But students do not work on their basics and then struggle. Therefore, to solve these problems effectively, you must make your basics strong beforehand. In addition, to make your basics strong, you must learn and revise them frequently. It is the thing that makes students struggle and think, “Who will do my math homework for me?”

Do Not Use the Shortcuts

You can never solve math with shortcuts, and tricks cannot be effective while using theorems. So, this is where students get stuck as they try to use these shortcuts to solve the questions and cannot get the appropriate answer. Thus, math problems require a step-by-step process to be solved. You can score points for performing a single step in this, so you must focus on the entire procedure.

Improve Your Analytical Skills

Problems related to circle theorems cannot be solved directly. It means you must first analyze the question and know which theorem will be applied and is suitable. Due to a lack of analytical skills, students cannot figure it out and thus cannot solve the issues. Therefore, you must practice more and more questions to polish your skills and get your hands on figuring out the correct theorem to use.

Conclusion

So, this is an end to the all-inclusive guide created on the popular math topic of circles. This write-up has everything, from the basic terminologies to tips to theorems you need to know before working on your academic tasks. Even after you face any difficulty and think, “Who will do my math homework“, you can seek help from professionals.