Tangent Circle Through Two Points

This example demonstrates how to construct a circle that passes through two given points and is tangent to a given line, a classic geometric construction problem. The core mathematical concepts involve the tangent property of a circle (radius perpendicular to tangent), the condition that the distance from the center to each point equals the radius, and the use of geometric loci to determine the center. The construction uses the Line command to create a reference line and the Point command to mark two target points A and B; then auxiliary lines (such as perpendicular bisectors or angle bisectors) are used to locate the center C, and a circle is drawn with center C and radius equal to the distance to the tangent point. This example is suitable for middle or high school geometry lessons on tangents, loci, and compass-and-straightedge constructions, and can be used for dynamic exploration of how the number and position of solutions vary with the configuration.