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Welcome to Geometry Proposed Problems!
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maintained by Antonio Gutierrez.
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Proposed Problems - Table of Content
(Page 1 of 3): Level: High
School, SAT Prep, College geometry.
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165. |
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Proposed Problem
165. Parallelogram, Diagonal, Triangles, Areas.
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164. |
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Proposed Problem
164. Parallelogram, Trapezoid, Diagonal, Triangles, Areas.
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163. |
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Proposed Problem
163. Trapezoid, Diagonals, Triangles, Areas.
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162. |
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Proposed Problem
162. Parallelogram, Triangles, Areas.
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161. |
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Proposed Problem
161. Parallelogram, Midpoints, Octagon, Areas.
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160. |
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Proposed Problem
160. Triangle, Incircle, Incenter, Circumcircle, Circumcenter, Inradius.
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159. |
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Proposed Problem
159. Distances from the Circumcenter to the Incenter and the Excenters.
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158. |
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Proposed Problem
158. Relation between the Circumradius, Inradius and Exradii of a triangle.
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157. |
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Proposed Problem
157. Distance from the Circumcenter to the Excenter.
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156. |
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Proposed Problem
156. Triangle, Circumradius, Exradius, Chord, Secant line.
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155. |
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Proposed Problem
155. Euler's Theorem: Distance from the Incenter to the Circumcenter.
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154. |
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Proposed Problem
154. Triangle, Inradius, Circumradius, Chord.
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153. |
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Proposed Problem
153. Circumscribed Quadrilateral, Diagonals Concurrent with Chords.
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152. |
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Proposed Problem 152. Circumscribed Quadrilateral, Diagonal, Chord, Proportion.
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151. |
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Proposed Problem
151. Quadrilateral, Area, Trisection of Sides.
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150. |
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Proposed Problem
150. Quadrilateral, Area, Trisection of Sides.
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149. |
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Proposed Problem
149. Quadrilateral, Area, Midpoints.
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148. |
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Proposed Problem
148. Quadrilateral, Area, Midpoints.
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147. |
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Proposed Problem
147. Quadrilateral, Area, Midpoints, Triangle.
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146. |
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Proposed Problem
146. Varignon's Theorem: Quadrilateral, Midpoints, Parallelogram, Area, Perimeter.
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145. |
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Proposed Problem
145.
Four Triangles, Incircle, Tangent and Parallel to Side, Incenters, Circumcenters.
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144. |
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Proposed Problem
144. Four Triangles, Incircle, Tangent and Parallel to Side, Inradii.
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143. |
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Proposed Problem
143. Four Triangles, Incircle, Tangent and Parallel to Side, Circumradii.
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142. |
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Proposed Problem
142. Four Triangles, Incircle, Tangent and Parallel to Side, Areas.
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141. |
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Proposed Problem
141. Triangle, Incircle, Tangent
, Parallel, Perimeters.
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140. |
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Proposed Problem
140. Triangle, Excircle, Tangent, Semiperimeter.
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139. |
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Proposed Problem
139. Triangle Area, Orthic Triangle, Semiperimeter, Circumradius.
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138. |
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Proposed Problem
138. Nagel's Theorem, Orthic Triangle, Altitudes, Circumradius, Perpendicular.
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137. |
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Proposed Problem
137. Orthic Triangle, Altitudes, Perpendicular, Incircle, Collinear Points, Parallelogram.
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136. |
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Proposed Problem
136. Orthic Triangle, Altitudes, Perpendicular, Concyclic Points.
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135. |
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Proposed Problem
135. Orthic Triangle, Altitudes, Perpendicular, Parallel
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134. |
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Proposed Problem
134. Orthic Triangle, Altitudes, Angle Bisectors, Orthocenter, Incenter.
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133. |
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Proposed Problem
133. Triangle, Angle Bisectors,
Collinear Points.
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132. |
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Proposed Problem
132. Triangle, 60 degree,
Orthocenter, Congruence, Midpoint.
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131. |
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Proposed Problem
131. Van Aubel Theorem, Concurrent Cevians, Sum of Ratios.
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130. |
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Proposed Problem
130. Triangle, Concurrent Cevians, Sum of Ratios.
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129. |
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Proposed Problem
129. Triangle, Concurrent Cevians, Sum of Ratios.
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128. |
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Proposed Problem
128. Incenter of a Triangle, Angle Bisectors, Sum of Ratios.
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127. |
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Proposed Problem
127. Centroid and Incenter of a Triangle,
Parallel, Proportions.
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126. |
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Proposed Problem
126. Incenter of a Triangle, Angle Bisector, Proportions.
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125. |
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Proposed Problem
125. Area of Triangle, Star,
Trisection of Sides.
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124. |
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Proposed Problem
124. Area of triangle,
Similarity, Trisection of Sides.
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123. |
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Proposed Problem
123. Area of triangle,
Similarity, Trisection of Sides.
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122. |
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Proposed Problem
122. Marion Walter's Theorem.
Area of triangle and Hexagon, Trisection of Sides.
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121. |
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Proposed Problem
121. Similarity and Area
of triangle, Trisection of Sides.
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120. |
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Proposed Problem
120. Area of triangle,
incenter, excircles,
tangent.
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119. |
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Proposed Problem
119. Area of triangle,
incenter, excircle,
tangent.
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118. |
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Proposed Problem
118. Area of triangle,
incenter, excenter,
tangent.
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117. |
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Proposed Problem
117. Area of triangle,
incenter, excircles,
tangent.
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116. |
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Proposed Problem
116. Area of triangle, excircles,
tangent.
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115. |
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Proposed Problem
115. Area of triangle, excircles,
tangent.
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114. |
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Proposed Problem
114. Area of triangle, incircle,
excircle.
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113. |
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Proposed Problem
113. Area of triangle, incircle,
excircle.
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112. |
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Proposed Problem
112. Area of square and triangle.
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111. |
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Proposed Problem
111. Orthogonal Circles.
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110. |
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Proposed Problem
110. Area of Contact Triangle.
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109. |
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Proposed Problem
109. Angles, Right Triangle, Cevian.
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108. |
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Proposed Problem
108. Angles, Triangle, Median.
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107. |
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Proposed Problem
107. Angles, Triangle. Cevian.
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106. |
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Proposed Problem
106. Angles, Triangle. Cevian.
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105. |
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Proposed Problem
105.Angles, Triangle. Interior
Point. |
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104. |
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Proposed Problem
104. Angles, Triangle.
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103. |
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Proposed Problem
103.Equilateral Triangle Area,
Interior Point, Heron's Formula.
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102. |
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Proposed Problem
102.Equilateral Triangle Area,
Interior Point. |
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101. |
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Proposed Problem
101.Equilateral Triangle,
Pythagorean Theorem, Angles.
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100. |
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Proposed Problem
100. Circle Area, Archimedes' Book of Lemmas.
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 "A
great discovery solves a great problem, but there is a grain of
discovery in the solution of any problem. Your problem may be
modest, but if it challenges your curiosity and brings into play
your inventive faculties, and if you solve it by your own means,
you may experience the tension and enjoy the triumph of
discovery. Such expert experiences at a susceptible age may
create a taste for mental work and leave their imprint on mind
and character for a lifetime." George Polya, 1944.
"Four phases trying to find the
solution, we may repeatedly change our point of view, our way of
looking at the problem. We have to shift our position again and
again. Our conception of the problem is likely to be rather
incomplete when we start the work; our outlook look is different
when we have made some progress; it is again different when we
have almost obtained the solution. In order to group
conveniently the questions and suggestions of our list, we shall
distinguish four phases of the work. First we have to
understand the problem; we have to see clearly what is required.
Second, we have to see how the various items are connected,
how the unknown-known is linked to the data in order to obtain
the idea of the solution, to make a plan.
Third, we carry out our plan. Fourth, we look back at
the completed solution, we review and discuss it." George Polya,
1944.
Exercise your brain. Solve these
problems about
congruence of line segments, angles, triangles,
circumferences, similarity, and areas and lift up your
geometry skills. Designed for high-school students, college
geometry, SAT preparation and teachers with an interest in
geometry problem-solving.
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