When constructing a circle that touches both a given circle and a straight line, you can follow a straightforward method that balances the positioning of the new circle. Here’s a general approach:
- Draw the Given Circle and Line: Start by drawing the given circle and the straight line, making sure they are positioned clearly in relation to each other.
- Identify the Point of Tangency on the Line: Choose or mark the point where the new circle will touch the straight line. This point will act as the base for the construction.
- Draw a Perpendicular Line: From the point of tangency on the straight line, draw a perpendicular line that extends towards the circle.
- Calculate the Radius: The distance between the center of the given circle and the point where the perpendicular line meets the straight line will help in determining the radius of the new circle. Ensure that the radius allows the new circle to touch both the given circle and the straight line.
- Draw the New Circle: Using the calculated radius and the point where the perpendicular line meets the straight line, draw the new circle. Make sure it touches both the given circle and the line at the marked point.
This construction requires precision, but once mastered, it can be applied in various geometric tasks.
If you found this method useful or need further clarification, feel free to drop a comment below. I’m here to help!
