This code creates a "snapping" effect that helps users easily construct a perfect equilateral triangle.[br][br]In simple terms, the code says: "If the user drags the vertex A very close to a pre-calculated perfect spot (A_1 or A_2), then automatically move A to that exact spot."

This script runs continuously in the [code]OnUpdate [/code]tab for point [code]A[/code], meaning it checks the condition every time [code]A[/code] is moved.[list=1][*][b]The Target Points ([code]A_1[/code] and [code]A_2[/code]):[/b] Before writing this script, the developer would have created two hidden points, [code]A_1[/code] and [code]A_2[/code]. These points represent the [b]two mathematically perfect locations[/b] where vertex [code]A[/code] would form an equilateral triangle with the other two vertices (let's call them [code]B[/code] and [code]C[/code]).[/*][*][b]The Snapping Zone:[/b] The [code]Distance(A, A_1) < 0.2[/code] part creates an invisible "snapping zone" or radius around the target point [code]A_1[/code]. The number [b][code]0.2[/code][/b] is the [b]threshold[/b]; you can make it larger for a more accurate snap or smaller for greater precision.[/*][*][b]The Action:[/b][list][*][code]If(Distance(A, A_1) < 0.2, SetValue(A, A_1))[/code]: This line checks if the draggable point [code]A[/code] has entered the snapping zone around the first target point [code]A_1[/code]. If it has, the [b][code]SetValue(A, A_1)[/code][/b] command is executed, which instantly moves [code]A[/code] to the exact coordinates of [code]A_1[/code], creating a perfect equilateral triangle.[/*][*]The second line does the exact same thing for the other possible target point, [code]A_2[/code].[/*][/list][/*][/list]An analogy is to think of the perfect spots [code]A_1[/code] and [code]A_2[/code] as having small, invisible [b]magnets[/b]. When you drag the vertex [code]A[/code] close enough, it gets pulled in and [b]locks perfectly into place[/b].

There are a few ways to create these hidden target points. The most classic method uses intersecting circles:[list=1][*][b]First Circle:[/b] Select the Circle tool. Create a circle with its center at point [b]B[/b] and its radius extending to point [b]C[/b]. This ensures every point on this circle is the correct distance from B.[/*][*][b]Second Circle:[/b] Create another circle with its center at point [b]C[/b] and its radius extending to point [b]B[/b].[/*][*][b]Find the Intersections:[/b] The two points where these circles intersect ([code]A_1[/code] and [code]A_2[/code]) are the only two locations in the plane that are the correct distance from [i]both[/i] B and C to form an equilateral triangle.[/*][/list]Your idea of using a perpendicular bisector is a great start because it correctly identifies the line of symmetry for an isosceles triangle. To adapt it for an [b]equilateral[/b] triangle, the height must be precise. The height of an equilateral triangle with side length [code]s[/code] is [code](s  √3) / 2[/code]. So, you would construct a circle on the perpendicular bisector with a radius of [code](length of base * √3) / 2[/code] to find the perfect spots. The two-circle method is often simpler to construct in GeoGebra.