Step 1: Find the circumference of the circle

          NOTE: Circumference of the circle =   2 \pi r

          EXAMPLE: Circumference = 2 \pi r

                                                      =   2 \pi(15)

                                                      = 30 \pi

Step 2: Identify the type of the triangle

          NOTE: The triangle are congruent because they are radii of the same circle.

                        So, \triangle APB is isosceles, and the

                          angles opposite the congruent sides are  congruent to each other.

          EXAMPLE:   \angle A = \angle B

Step 3: Add the interior angles of a triangle up to 180\degree, to find the unknown angle.

             \angle A + \angle B + \angle P = 180\degree

             38\degree + 38\degree + \angle P = 180\degree

             \angle P = 104\degree

Step 4: Calculate the arc length.

Arc length:

Step 1: Note down the given values

Step 2: Set up the formula for arc length. 

NOTE: The formula is arc length= 2 \pi (r)(\frac{\theta }{360}) ,

where {\displaystyle r} equals the radius of the circle and {\displaystyle \theta } equals the measurement of the arc’s central angle, in degrees.


Arc length = r * \theta

Step 3: Plug the length of the circle’s radius into the formula.

Step 4: Plug the value of the arc’s central angle into the formula. 

Step 5: Simplify the equation to find the arc length

NOTE: Use multiplication and division to simplify the equation.


Area of the circle.

Step 1: Identify the known or given information.

Step 2: Set up a formula for the sector area

            NOTE: A ratio will need to be constructed. Recall that a circle is composed

            of 360 degrees. Therefore, the following ratio can be made,

                         \frac{\theta}{360} = \frac{\text{sector area} (A_C)}{\text{Total area} (A_T)}

            Sector area = \frac{\theta}{360} * \pi r^2 (since area = \pi r^2)

                where, \theta = Central angle.

Step 3: Plug the sector’s central angle measurement into the formula.  

Step 4: Plug the sector’s radius measurement into the formula.  

Step 5: Solve for the area:

            EXAMPLE: Sector area = \frac{\theta}{360} * \pi r^2 (since area = \pi r^2)

                              Sector area = \frac{60}{360}*\left(3.14\right)\left(5\right)^2

                                  Sector area = 13.09 cm^2