Math Help - geometry

1. geometry

construct an inscribed circle in a circular sector.Explain each step

2. Originally Posted by bjhopper
construct an inscribed circle in a circular sector.Explain each step
I hope this doesn't come too late...

I assume that you have a circular sector.

1. Construct the angle bisector passing through S. The intersection of the angle bisector and the arc of the sector is Z. Z must be a tangent point of the circle in question.

2. Choose an arbitrary point $M_a$ on the angle bisector which is the midpoint of the arbitrary circle $c_a$ with the radius $r = |\overline{M_a Z}|$ (in blue)

3. Draw a line through $M_a$ perpendicular on one leg of the sector. This line intersects the circle $c_a$ in $T_a$

4. Draw a line $ZT_a$ which intersect the leg of the sector in T. This is a tangentpoint of the circle c which you are looking for.

5. A parallel to $M_aT_a$ through T intersects the angle bisector in M which is the midpoint of the circle c. (in red)

Actually the construction uses similar triangles (indicated by different patterns in red) and the point Z as the fixpoint of a central dilation.

3. geometry

posted by bjhopper