Some Construction Problems

These problems use our tools, but may not have been done in the course up to now.

Problem 1

This figure contains 3 lines, two of which are parallel. Construct all circles that are tangent to all 3 lines.

Problem 2

This figure contains 2 parallel lines and a point. Construct all circles that pass through the point and that are also tangent to the two lines.

Problem 3

This figure contains 2 parallel lines and a point on one line. Construct all circles that pass through the point and that are also tangent to the two lines.

Problem 4

This figure contains two intersecting lines and a point on one line. Construct all circles that pass through the point and that are also tangent to the two lines.

Problem 5

This figure contains a circle and a point A on the circle.

Sketchpad Construction

• Construct the circle b through point B so that it is tangent to the given circle at A. Then drag B around to positions like that of C and see how the relationships of the two circles changes while they still remain tangent.

Straightedge and Compass on Paper Construction

• Construct the circle b through point B so that it is tangent to the given circle at A.
• Construct the circle b through point C so that it is tangent to the given circle at A.

Problem 6

Construct a square with the same area as this rectangle.