Intro to Circles

​TEKS

 (12) Circles. The student uses the process skills to understand geometric relationships and apply theorems and equations about circles. The student is expected to:

    (A) apply theorems about circles, including relationships among angles, radii, chords, tangents, and secants, to solve non-contextual problems;

    (B) apply the proportional relationship between the measure of an arc length of a circle and the circumference of the circle to solve problems;

    (C) apply the proportional relationship between the measure of the area of a sector of a circle and the area of the circle to solve problems;

    (D) describe radian measure of an angle as the ratio of the length of an arc intercepted by a central angle and the radius of the circle; and

    (E) show that the equation of a circle with center at the origin and radius r is x² + y² = r² and determine the equation for the graph of a circle with radius r and center (h, k), (x - h)² + (y - k)² = r² .

2π (rad) = 360⁰

​Radians and Degrees

x² + y² = r²

​Equation of a circle

​Circles on a coordinate plane

• In order to write the equation of a line, you need the center point and either the radius or a point on the circumference of the circle.

​Center point not at origin point

• If the center point is not at origin point we can use:
  (x-h)² + (y-k)² = r² where (h,k) are the coordinates of the center point.

Remember!!!

• (x-h)² moves right

• (y-k)² moves up

​Let's draw some angles!

Partners:

• Work with a partner to draw 4 circles based off of equations found in Canvas

• Yes, it is for a grade.

Independent:

• Work by yourself to complete the quizzes on Canvas:

  • Equations of Circles

  • Converting Radians & Degrees.