Similar circles 1 APS
1. Drag the sliders up and down to make the pre-image and image circles different sizes. How does the scale factor change as you move the sliders?
2. Use the dilate button to enlarge or reduce the pre-image with the given scale factor. Describe the dilated pre-image.
Use the translate button to slide the dilated pre-image over to the image. Does the new circle map onto the image?
Explain how all circles are similar.
Exploring Inscribed & Circumscribed Angles APS
Construction: Circumscribed and Inscribed Circles APS
Construction-1: Circumscribed Circle
Construct a circumscribed circle to the given triangle. Take a screen shot of your final image and save it into google drive.
Construction 2: Inscribed Circle
Construct an inscribed circle to the given triangle. Take a screen shot of your final image and save it into google drive.
Construction: Tangents to a Circle from a Point Outside the Circle APS
This applet shows how to construct tangents to a circle from a point outside the circle.
1. What happens when the point A is inside the circle ?[br]2. What happens when the point A coincides with point M ?
Exploration: Arc Length and Sector Area APS
Exploration: Circumference and Area of a Circle APS
This applet illustrates formulas for the circumference by rolling a circle along a line, then measuring the length in units of the diameter, or the radius.[br][br]Check the "Show rolling circle" box, then roll the circle with the slider labeled "Roll circle".[br]Check "Show C measured with r, d."[br][br]This leads to a formula for the area of a circle, too. Cut it apart into sectors, and rearrange into a "parallelogram".[br][br]Check the last three boxes to see this.
Formulas:[br][br]Circumference = [math]\pi[/math] diameter (that is, [math]C=\pi d[/math])[br]Circumference = 2[math]\cdot\pi\cdot[/math]radius (that is, [math]C=2\pi r[/math])[br][br]Area = Circumference [math]\cdot[/math] radius [br]Area = [math]\pi\cdot[/math] radius squared (that is, [math]A=\pi r^2[/math])
Sections of Rectangular Prisms (Cuboids) APS
Drag the blue points to see the different sections of the rectangular prism (cuboid).
Anthony Or. GeoGebra Institute of Hong Kong