Proposed Problem 451.
Triangle, Median, Congruence, Proportional Segments.

Proposed Problem 452.
Triangle, Circle, Tangent, Proportional Segments.

Proposed Problem 453.
Intersecting Circles, Tangent, Circular Segment, Congruence, Area.

Proposed Problem 454.
Triangle, Incircle, Inradius, Tangent, Circle, Radius, Metric Relations.

Proposed Problem 455.
Rhombus, Inscribed Circle, Angle, Chord, 45 Degrees.

Proposed Problem 456.
Three tangent circles, Center, Chord, Secant, Collinear.

Proposed Problem 457.
Triangle, First Brocard Point, Congruent angles, Circle, Circumradius.

Proposed Problem 458.
Square, Semicircle, Circular Sector, Internal Common Tangent, Measurement.

Proposed Problem 459.
Right triangle, Squares, Distance, Measurement.

Proposed Problem 460.
Circle, Tangent, Perpendicular, Radius, Distance, Measurement.