On Geogebra make a circle of any radius and change its color to red so it...

On Geogebra make a circle of any radius and change its color to red so it will stand you as your circle of inversion. Make a triangle that is completely outside of your circle of inversion that does not touch the circle of inversion and then find the inversion of the triangle over the red circle. You can use the Geogebra tools for any of the constructions we already know how to do (such as perpendicular lines or midpoints) instead of having to only use the compass and segment tools. Here are two hints: 1. You need to find where all three of the vertices of your triangle go. 2. The edges of your triangle are straight, but as you have seen with the last activity, a line segment should end up being the arc of a circle when it is inverted. The sides of your inverted triangle will not be straight. Think about where the midpoint of the triangle's edges go to get the shape correct.
Leave the lines you needed to construct your inversion visible and paste your construction into your homework document.

Expert Solution

On Geogebra make a circle of any radius and change its color to red so it will stand you as your circle of inversion. Make a triangle that is completely outside of your circle of inversion that does not touch the circle of inversion and then find the inversion of the triangle over the red circle. You can use the Geogebra tools for any of the constructions we already know how to do (such as perpendicular lines or midpoints) instead of having to only use the compass and segment tools. Here are two hints: 1. You need to find where all three of the vertices of your triangle go. 2. The edges of your triangle are straight, but as you have seen with the last activity, a line segment should end up being the arc of a circle when it is inverted. The sides of your inverted triangle will not be straight. Think about where the midpoint of the triangle's edges go to get the shape correct.
Leave the lines you needed to construct your inversion visible and paste your construction into your homework document.

solution: Inversion in a circle, K of radius R, of a circle. The points, a, b, c, and d, are inverted in K to A, B, C, and D, respectively. If qa denotes the distance from q to a, and qA the distance from q to A, from the definition of inversion in k, qA=R*R/qa. The circle then constructed through the points A, B, and C makes clear that any circle that doesn't go through the center of K under inversion in K is a circle!Points a and p can be dragged to move the circle inside K. The points b, c, or d can also be dragged.

venereology answered 1 year ago

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