__Instruction:__ Construct a circle that is tangent to the three given lines. Two of the lines are parallel.

__Goal:__ 4L 6E

Available tools:

- Move
- Point
- Line
- Circle
- Perpendicular Bisector
- Perpendicular
- Angle Bisector
- Parallel
- Non-collapsing Compass
- Intersect

__Pack:__ Eta

__Previous level:__ 7.7

__Next level:__ 7.9

## 4L solution[]

Given the intersections of the lines A and B.

- Construct the angle bisector of ∠CAB, with C an arbitrary point on one of the parallel lines.
- Construct the angle bisector of ∠ABD, with D an arbitrary point on the other parallel line and on the same side as C from the third given line, intersecting the angle bisector of ∠CAB at E
- Construct the perpendicular to AB through E, intersecting AB at F
- Construct the circle with center E and radius EF

## 6E solution[]

Given the intersections of the lines A and B.

- Construct the circle with center A and radius AB, intersecting the parallel line through A at C and D
- Construct line BC
- Construct the circle with center C and radius BC
- Construct the circle with center D and radius CD, intersecting circle C at E and F
- Construct line EF, intersecting BC at G and AC and H
- Construct the circle with center G and radius GH

## 2V solution[]

From the 4L solution:

- Construct the angle bisector of ∠GAB, with G an arbitrary point on AC and on the other side of C from A.
- Construct the angle bisector of ∠ABH, with H an arbitrary point on BD and on the other side of D from B, intersecting the angle bisector of ∠GAB at I
- Construct the perpendicular to AB through I, intersecting AB at J
- Construct the circle with center I and radius IJ