Triangles: Theorems and Problems 7a

Geometry Problem 1187
Triangle, Quadrilateral, Midpoints, Area.

Geometry Problem 1186
Right Triangle, Square, Inscribed Circle, Tangent, Quadrilateral, Area.

Geometry Problem 1185
Similar Rectangles, Four Quadrilaterals, Sum of the Areas, Metric Relations.

Geometry Problem 1184
Right Triangle, Square, Inscribed Circle, Tangent, Concurrent Lines.

Geometry Problem 1180
Quadrilateral, 120 Degrees, Diagonals, Perpendicular.

Geometry Problem 1179
Triangle, Centroid, Transversal, Sum of Ratios, Sides.

Geometry Problem 1178
Triangle, Angle Bisector, Metric Relations.

Geometry Problem 1177
Triangle, Two Angle Bisectors, Metric Relations.

Geometry Problem 1174
Triangle, Quadrilateral, Double, Triple, Angle, Congruence, Excenter, Angle Bisector.

Geometry Problem 1173
Triangle, Cevian, Angle, Congruence, Similarity.

Geometry Problem 1172
Cyclic Quadrilateral, Circle, Secant, Triangle, Similarity, Metric Relations.

Geometry Problem 1171
Area of a Triangle in terms of the three altitude or heights h_a, h_b, h_c.

Geometry Problem 1170
Area of a Triangle in terms of the three sides, a-b-c.

Geometry Problem 1169
Complete Quadrilateral, Orthocenters of the Component Triangles, Collinear Points, Ortholine, Steiner-line, Orthocentric line.

Geometry Problem 1167.
Triangle, Circle, Circumcircle, Perpendicular, 90 Degrees, Collinear Points.

Geometry Problem 1166.
Triangle, Circles, Diameters, Secant, Midpoint, Congruence.

Geometry Problem 1165.
Right Triangle, Circle, Center, Radius, Cathetus, Perpendicular, 90 Degrees, Perimeter, Metric Relations.

Geometry Problem 1164.
Triangle, Angle Bisector, Cevian.

Geometry Problem 1163.
Isosceles Triangle, Congruence, Double Angle, Circle, Concyclic Points, Circumcenter, Perpendicular, Angle Bisector.

Geometry Problem 1162.
Triangle, Congruence, Double Angle, Parallel Lines, Circle, Circumcenter.

Geometry Problem 1161.
Scalene Triangle, 60 Degrees, Angle, Orthocenter, Circumcenter, Equilateral Triangle, Congruence.

Geometry Problem 1160.
Triangle, Three Squares, Area, Equivalent Triangles.

Geometry Problem 1159.
Triangle, Circumcircle, Sagitta, Chord, Arc, Metric Relations.

Geometry Problem 1158.
Four Tangent Circles, Tangent Chord, Radius, Metric Relations.

Geometry Problem 1157.
Four Circles, Mutually Tangent, 90 Degrees, Radius, Metric Relations.

Geometry Problem 1156.
Square, Tangent Line, 90 Degrees, Metric Relations.

Geometry Problem 1155.
Right Triangle, Altitude, Incenter, Incircle, Area.

Geometry Problem 1153.
Triangle, Angle Bisectors, Perpendicular, Congruence.

Geometric Art: Isolines, the Valknut, three Interlocked Triangles, Geometry for Kids, Software, iPad, Parallel Lines

Geometry Problem 1152.
Triangle, Quadrilateral, Angle, 10, 20, 30 Degrees.

Geometric Art: Isolines, Triquetra, Celtic Knotwork, Trefoil Knot, Parallel Lines, Geometry for Kids, Software, iPad, Parallel Lines

Geometry Problem 1151.
Circle, Diameter, Chord, Perpendicular Secants, 90 Degrees, Metric Relations.

Geometry Problem 1150.
Circle, Perpendicular Secants, 90 Degrees, Congruence.

Geometry Problem 1149.
Isosceles Triangle, Altitude, Cevian, Incircles, Tangent, Congruence.

Dynamic Geometry Problem 1148
Static Geometry Problem 1148.
Right Triangle, Incircle, Circumcircle, Tangent, Radius. GeoGebra, HTML5 Animation for Tablets (iPad, Nexus).

Geometry Problem 1147.
Scalene Triangle, Orthocenter, Circumcenter, Congruence, Equilateral Triangle.

Geometry Problem 1146.
Triangle, Interior Point, 10, 20, 30, 130 degrees, Congruence.

Geometry Problem 1145.
Three Squares, Midpoints.

Geometry Problem 1144.
Three Equal Squares, Diagonals, Perpendicular, 90 Degrees, Angle Bisector.

Geometry Problem 1143.
Triangle, Circumcircle, Tangent Line, Reflection of a Point over a Line, Tangent Circles, Collinear Points.

Geometry Problem 1142.
Cyclic Quadrilateral, Isogonal Lines, Circle, Center, Radius, Perpendicular Bisector, Circumcenter.

Geometry Problem 1141.
Inscribed Pentagon, Circle, Triangle, Congruence, Midpoint, Concurrency.

Geometry Problem 1140.
Triangle, Circumcircle, Circle, Center, Collinear Points.

Geometry Problem 1139.
Triangle, Circumcircle, Angle Bisector, Parallel Lines, 90 Degrees, Concurrent Lines.

Geometry Problem 1138.
Square, Perpendicular, Angle, 90 Degrees, Triangle, Congruence.

Geometry Problem 1137.
Triangle, Circumcircle, Circumcenter, Orthocenter, Midpoint, Arc, Collinear Points, Tangent Circles.

Geometry Problem 1136.
Triangle, Circumcircle, Orthocenter, Midpoint, Arc, 90 Degrees, Angle.

Geometry Problem 1135.
Intersecting Circles, Secant, Parallel Line, 90 Degrees, Similar Triangles.

Geometry Problem 1134.
Tangent Circles, Tangent Line, Triangle, Circumcircle, Circumcenter.

Geometry Problem 1133.
Circle, Chord, Tangent, Circumcircle, Similarity, Equal Product.

Geometry Problem 1132.
Triangle, Excircle, Tangency Point, Parallel, Midpoint.

Geometry Problem 1131.
Triangle Area, Two Cevians, Equal Product of Areas.

Geometry Problem 1129.
Isosceles Triangle, Circumcenter, Incenter, Parallel Lines, Perpendicular Lines.

Geometry Problem 1128.
Right Triangles, Medians, Parallel, Angles, Congruence, Half the measure.

Geometry Problem 1127.
Triangle, Circumcircle, Tangent, Circle, Diameter, Midpoint, Perpendicular, 90 Degrees.

Geometry Problem 1126.
Equilateral Triangle, Circumcircle, Metric Relation, Harmonic Mean.

Geometry Problem 1125.
Triangle, Four Equilateral Triangles, Centroid, Midpoint.

Geometry Problem 1124.
Triangle, Median, Two Squares, Area.

Geometry Problem 1123.
Hexagon, Triangle, 90 Degrees, Perpendicular Lines, Vertices, Area.

Geometry Problem 1122.
Triangle, 90 Degree, Perpendicular Lines, Orthocenter, Altitude, Midpoint, Collinear Points.

Geometry Problem 1120.
Isosceles Right Triangle, 120 Degree, Angle, Equilateral, Metric Relations.

Geometry Problem 1119.
Quadrilateral, Similar Triangles, Midpoints, Equal Ratio, Angles.

Geometry Problem 1118.
Right Triangle, Angle Trisection, Concyclic Points, Cyclic Quadrilateral.

Geometry Problem 1117.
Right Triangle, Angle Trisection, 90 Degrees, Parallel Lines.

Geometry Problem 1116.
Right Triangle, Angle Trisection, 90 Degrees, Perpendicular Lines.

Geometry Problem 1115.
Right Triangle, Angle Trisection, Equilateral Triangle.

Geometry Problem 1114.
Right Triangle, Angle Trisection, Isosceles, Congruence.

Geometry Problem 1113.
Triangle, Perpendicular Bisector, 90 Degrees, Circle, Concyclic Points, Cyclic Quadrilateral.

Geometry Problem 1112.
Triangle, Excenters, Circumcircle, Circle, Hexagon, Area.

Geometry Problem 1107.
Triangle, Circumcircle, Circle, Radius, Tangent, Chord, Congruence.

Geometry Problem 1106.
Regular Hexagon, Congruence, Diagonal, Collinear Points.

Geometry Problem 1105.
Triangle, Incircle, Excircle, Cevian, Tangent, Congruence, Geometric Mean.

Geometry Problem 1104.
Right Triangle, Incircle, Circumcircle, Inscribed Circle, Radius, Tangent.

Geometry Problem 1103.
Right Triangle, Incircle, Inscribed Circle, Radius, Geometric Mean, Sangaku, Japanese, Metric Relations.

Geometry Problem 1102.
Right Triangle, Incircle, Tangency Point, 90 Degree, Cathetus, Metric Relations.

Geometry Problem 1101.
Triangle, Parallel Lines, Circle, Incircle, Inradius, Radius, Angle.