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Welcome to Geometry Proposed
Problems! Site created and maintained by Antonio
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Proposed Problems - Table of Content (Page 1 of 6)
NCTM Processes: Problem Solving, Reasoning
& Proof, Communications, Connections, and Representation
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Proposed Problem
313.
Circle, Chord, Tangent, Perpendicular, Geometric Mean. |
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Proposed Problem
312.
Cyclic quadrilateral, Side extensions, Tangents. |
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Proposed Problem
311.
Circle Inscribed in a Semicircle, Chord, Diameter. |
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Proposed Problem
310.
Circle Inscribed in a Semicircle, 45 Degrees Angle. |
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Proposed Problem
309.
Regular Nonagon or Enneagon, Diagonals, Side. |
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Proposed Problem
308.
Regular Nonagon or Enneagon, Midpoints, Side, Arc, Angle. |
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Proposed Problem
307.
Regular Nonagon or Enneagon, Midpoints, Side, Arc, Angle. |
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Proposed Problem
306.
Square, Triangles, Angles, Sides. |
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Proposed Problem
305.
Square, Triangles, Angles, Sides. |
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Proposed Problem
304.
Triangle, Angle bisector of 120 degrees. |
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Proposed Problem
303.
Triangle, Angle bisector of 90 degrees. |
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Proposed Problem
302.
Triangle, Angle bisector of 60 degrees. |
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Proposed Problem
301.
Tangents to a circle, Secants, Square. |
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Proposed Problem
300.
Tangents to a circle, Secants, Square. |
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Proposed Problem 299.
Intersecting Circles, Chord, Secant, Midpoint, Congruence. |
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Proposed Problem 298.
Intersecting Circles, Chord, Secant, Midpoint, Congruence. |
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Proposed Problem 297.
Intersecting Circles, Chord, Secant, Radius, Angle, Perpendicular. |
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Proposed Problem 296.
Intersecting Circles, Chord, Radius, Angle, Perpendicular. |
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Proposed Problem 295.
Archimedean Twin Circles, Arbelos, Semicircles, Harmonic Mean, Radii, Perpendicular. |
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Proposed Problem 294.
Right triangle, Circumcenter, Excenter, Hypotenuse, Perpendicular. |
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Proposed Problem 293.
Inscribed Quadrilateral, Perpendicular, Rectangle, Isosceles Right triangle, Area, Similarity. |
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Proposed Problem 292.
Triangle, Parallel, Congruence, Similarity. |
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Proposed Problem 291.
Triangle, Circle, Circumradius, Perpendicular. |
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Proposed Problem 290.
Internally Tangent circles, Radius, Perpendicular, Tangent. |
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Proposed Problem 289.
Externally Tangent circles, Radius, Perpendicular, Tangent. |
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Proposed Problem 288.
Tangent circles, Harmonic Mean, Radius, Diameter. |
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Proposed
Problem 287.
Regular Octagon. |
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Proposed
Problem 286.
Square, Midpoints, Octagon. |
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Proposed Problem 285.
Circular Sector 90 degrees, Semicircles, Circle, Tangent, Radius. |
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Proposed Problem 284.
Circular Sector 90 degrees, Semicircles, Tangent, Radius. |
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Proposed Problem
283.
Circular Sector 90 degrees, Semicircle, Circle inscribed, Radius. |
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Proposed Problem
282.
Right Triangle, Cevian, Angles, Perpendicular, Congruence.
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Proposed Problem
281.
Triangles, Angles, Isosceles, Equilateral. |
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Proposed Problem
280.
Quadrilateral, Perpendiculars, Area of Squares. |
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Proposed Problem
279.
Tangent Circles, Common External Tangent, Chords, Inradius. |
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Proposed Problem
278.
Tangent Circles, Common External Tangent, Chord. |
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Proposed Problem
277.
Tangent Circles, Common External Tangent. |
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Proposed Problem
276.
Square, 90 degree Arcs, Circle, Radius. |
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Proposed Problem
275.
Right Triangle, Circumcircle, Sagitta, Inradius. |
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Proposed Problem
274.
Isosceles Triangle, 80-80-20, Angles. |
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Proposed Problem
273.
Triangle, Perpendiculars, Area of Squares. |
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Proposed Problem
272.
Tangent Circles, the Cube of the Common external tangent. |
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Proposed Problem
271.
Tangent Circles, the Cube of the Common external tangent. |
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Proposed Problem
270.
Tangent Circles, Common external tangent, Fractional exponents. |
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Proposed Problem
269.
Right Triangle, Altitude, Perpendicular, Projection. |
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Proposed Problem
268.
Right Triangle, Catheti and Altitude. |
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Proposed Problem
267.
Right Triangle, Product of Catheti. |
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Proposed Problem
266.
Right Triangle, Altitude, Geometric Mean. |
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Proposed Problem
265.
Right Triangle, Pythagorean Theorem. |
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Proposed Problem
264.
Right Triangle, Altitude, Leg projection, Hypotenuse, Similarity, Geometric mean. |
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Proposed Problem
263.
Triangle, Median, Altitude, Orthogonal Projection, Sides. |
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Proposed Problem
262.
Regular Hexagon inscribed in a circle, sum of distances. |
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Proposed Problem
261.
Regular Pentagon inscribed in a circle, sum of distances.
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Proposed Problem
260.
Equilateral Triangle, Incircle, Tangency Points, Vertices, Distances, Squares.
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Proposed Problem
259.
Equilateral Triangle, Incircle, Tangency Points, Side, Distances, Squares.
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Proposed Problem
258.
Equilateral Triangle, Circumcircle, Point, Vertices, Side, Distances,
Squares.
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Proposed Problem
257.
Equilateral Triangle, Circumcircle, Point, Vertices, Side, Distances,
Squares.
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Proposed Problem
256.
Equilateral Triangle, Circumcircle, Point, Vertices, Distances.
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Proposed Problem
255.
Triangle, Centroid, Vertices, a Point, Distances, Squares.
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Proposed Problem
254.
Triangle, Centroid, Vertices, a Point, Distances, Squares.
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Proposed Problem
253.
Triangle, Centroid, Vertices, Distances, Squares.
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Proposed Problem
252.
Rectangle, isosceles right triangle, square, area.
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Proposed Problem
251.
Parallelogram, sides, diagonals, squares, areas.
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Proposed Problem
250.
Quadrilateral, sides, diagonals, midpoints, squares.
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Proposed Problem
249.
Triangle sides, medians, squares.
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Proposed Problem
248.
Napoleon's Theorem III. Inner and outer Napoleon triangles, Area.
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Proposed Problem
247.
Napoleon's Theorem II. Internal Equilateral triangles. Inner Napoleon
triangle.
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Proposed Problem
246.
Napoleon's Theorem I. External Equilateral triangles. Outer Napoleon
triangle.
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Proposed Problem
245. Parallelogram with Equilateral triangles.
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Proposed Problem
244. Square, Diagonals, Centers, Distance.
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Proposed Problem
243. Triangle with Equilateral triangles, Parallelogram.
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Proposed Problem
242. Triangle with Equilateral triangles, Parallelogram.
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Proposed Problem
241. Triangle with Equilateral triangles, Congruence.
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Proposed Problem
240. Triangle with Equilateral triangles, Parallelogram.
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Proposed Problem
239. Square, Midpoints, Lines, Congruence, Pythagoras.
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Proposed Problem
238. Square, Midpoints, Lines, Congruence.
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Proposed Problem
237. Quadrilateral, Midpoints, Exterior line, Perpendicular lines.
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Proposed Problem
236. Quadrilateral, Midpoints, Exterior line, Perpendicular lines.
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Proposed Problem
235. Parallelogram, Transversal line, Perpendicular lines.
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Proposed Problem
234. Parallelogram, Line through a vertex, Perpendicular lines.
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Proposed Problem
233. Parallelogram, Exterior line, Perpendicular lines.
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Proposed Problem
232. Parallelogram, Line through a vertex, Perpendicular lines.
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Proposed Problem
231. Triangle, Midpoints, Transversal, Perpendicular lines.
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Proposed Problem
230. Triangle, Midpoints, Transversal, Perpendicular lines.
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Proposed Problem
229. Triangle, Centroid, Transversal, Perpendicular lines. |
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Proposed Problem
228. Triangle, Midpoints, Exterior line, Perpendiculars lines.
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Proposed Problem
227. Triangle, Centroid, Exterior line, Perpendicular lines. |
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Proposed Problem
226. Triangle, Centroid, Perpendicular lines. |
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Problemas Propuestos de
Geometria en Espanol. |
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Proposed Problem
225. Viviani's Theorem Extension, Regular Polygon, Apothem, Distance. |
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Proposed Problem
224. Viviani's theorem, Isosceles triangle,
Altitude, Distances, Point on the extension of the base. |
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Proposed Problem
223. Viviani's theorem, Isosceles triangle,
Altitude, Distances. |
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Proposed Problem
222. Viviani's theorem, Equilateral triangle, Exterior point,
Altitude, Distances. |
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Proposed Problem
221. Viviani's theorem, Equilateral triangle, Interior point,
Altitude,
Distances. |
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Proposed Problem
220. Right Triangle, Altitude, Angle Bisector, Distance, Arithmetic Mean.
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Proposed Problem
219. Rhombus, Perpendiculars, Arithmetic Mean.
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Proposed Problem
218. Right triangle, Altitude and Projections. |
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Proposed Problem
217. Right triangle, Altitude and Projections.
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Proposed Problem
216. Quadrilateral, Angle Bisectors, and Concurrency.
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Proposed Problem
215. Quadrilateral, Angle Bisectors, and Cyclic Quadrilateral.
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Proposed Problem
214.
Quadrilateral and Angle Bisectors.
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Proposed Problem
213. Triangle, Incircle, Inradius, Semicircles, Common Tangents. |
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Proposed Problem
212. 120 Degree Triangle, Equilateral triangles, Areas.
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Proposed Problem
211. 60 Degree Triangle, Equilateral triangles, Areas.
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Proposed Problem
210. Triangle, Angles, Auxiliary Lines.
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Proposed Problem
209. Triangle, Incircles, Inradius. |
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Proposed Problem
208. Triangle, Excircles, Angles, 360 degrees. |
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Proposed Problem
207. Right Triangle, Hypotenuse, Inradius, Exradius relative to the hypotenuse. |
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Proposed Problem
206. Area of a Right Triangle, Inradius, andExradius relative to the hypotenuse. |
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Proposed Problem
205. Right Triangle Area, Exradii relatives to legs or catheti. |
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Proposed Problem
204. Right Triangle, Incircle, Excircles, Inradius, Exradii. |
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Proposed Problem
203. Right Triangle, Excircles, Exradii, Hypotenuse. |
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Proposed Problem
202. Right Triangle, Incirle, Excircles relatives to catheti, Points of Tangency, Exradius, Semiperimeter. |
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Proposed Problem
201. Right Triangle, Excircles, Points of Tangency, Exradius, Semiperimeter. |
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Proposed Problem
200. RightTriangle, Incircle, Excircles, Points of Tangency, Inradius. |
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Proposed Problem 199. Triangle, Quadrilateral, Angles.
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Proposed Problem
198. Triangle, Quadrilateral, Angles. |
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Proposed Problem
197. Area of a Triangle, Side, Inradius, and Exradius. |
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Proposed Problem
196. Triangle, Inradius and Exradii Formula. |
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Proposed Problem
195. Area of a Triangle, Inradius, Exradii. |
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Proposed Problem
194. Area of a Triangle, Semiperimeter, Exradius. |
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Proposed Problem
193. Area of a Triangle, Semiperimeter, Inradius. |
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Proposed Problem
192. Circle, Diameter, Chord, Perpendicular, Triangle, Area. |
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Proposed Problem
191. Triangle, Altitudes, Orthocenter, Squares, Areas. |
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Proposed Problem
190. Tangent circles, Tangent chord, Perpendicular, Distance. |
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Proposed Problem
189. Squares, Distances. |
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Proposed Problem
188. Square, Diagonal, 45 Degrees Angle. |
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Proposed Problem
187. Right Triangle, Altitude, Incenters, Circles,
Angles. |
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Proposed Problem
186. Right Triangle, Altitude, Incenters, Circles. |
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Proposed Problem
185. Trapezoid, Triangles and Angles. |
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Proposed Problem
184. Triangle and Angles. |
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Proposed Problem
183. Right Triangle, Hypotenuse Trisection Points, Squares of the Distances. |
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Proposed Problem
182. Overlapping Circles, Find an angle. |
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Proposed Problem
181. Circular Sector of 90 degrees, find an angle. |
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A great discovery solves a great problem, but there
is a grain
of discovery in the solution of any problem.
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