Geometry Problem 801
Equilateral Triangles, Cevian, Midpoint, Distance, Measurement, Metric Relations.

Geometry Problem 802
Scalene Triangle, Median, Perpendicular, Angle, Measurement.

Geometry Problem 803
Right Triangle, Altitude, Angle Bisector, Perpendicular, Measurement.

Geometry Problem 804
Butterfly theorem. Circle, Chord, Midpoints.

Geometry Problem 805, Stewart Theorem
Triangle, sides and a cevian.

Geometry Problem 806
Triangle, Points on sides, Circumcenter, Similarity.

Geometry Problem 807
Right Triangle Area, Incircle, Tangency Points, Semicircle Area.

Geometry Problem 808
Parallelogram, Perpendicular, Right Triangle, Semicircle Area, Diameter.

Geometry Problem 809: Trisecting a line segment.
With three circles and four lines.

Geometry Problem 810: Trisecting a line segment.
With two circles and eight lines.