Algrebra | Circle Theorems

Formulas

Circumfrerence = \$2\pir\$
Diameter = \$2r\$
Area = \$\pir^2\$

Lines

Chords: Line segment that connects two endpoints on a circle. If a chord passes through the center of a circle its known as a diameter
Tangent Line: Touches just one point at a curce.
Secant Line: A line the passes through two points of a curve.
Radius: half of diameter

Central Angle

\$m\angle ACB = mACB\$

Inscribed Angle

\$m\angle ABC = \frac{1}{2}m \overarc{AC}\$

Tangent-Chord Angle

\$m\angle ABC = \frac{1}{2}(m\overarc{AB})\$

Unit Circle

y: sine
x: cosine

Standard Circle Formula

\$(x -h)^2 + (y - k)^2 =r^2\$

h and k are the x and y coordinates of the center of the circle.

Drawing a Circle in C

Without Standard Circle Formula:

void drawCircle(SDL_Renderer *ren, float radius, SDL_Point center, uint32_t color)
{

    float x = 0;
    float y = 0;
    for(float i = 0; i < 2 * M_PI; i += 0.001f)
    {
        x = cos(2.0f * M_PI * i);
        y = sin(2.0f * M_PI * i);
        SDL_Rect point = {
            (x * radius) + center.x,
            (y * radius) + center.y,
            1,
            1
        };
        SDL_SetRenderDrawColor(ren, 0, 0, 0, 255);
        SDL_RenderFillRect(ren, &point);
    }
}