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![Geometry, Theorems and Problems](h_online_math_geometry_910.jpg)
Online Geometry Theorems and Problems. College, High School
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Geometry - Recent
Additions
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![Euclidean Geometry](euclidean_geometry_17.jpg) |
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![Problem 1433](../school-college/5/p1433-tangent-circles-line-midpoint-1.jpg) |
Geometry Problem 1433.
Tangent Circles, Diameter, Perpendicular, Midpoint, Measurement,
Poster Typography, iPad Apps. |
![Problem 1432](../school-college/5/p1432-tangent-circles-proportion-similarity-ipad-apps-1.jpg) |
Geometry Problem 1432.
Tangent Circles, Secant, Tangent Lines, Proportionality, Similarity,
Poster Typography, iPad. |
![Problem 1431](../school-college/5/p1431-apollonius-llc-triangle-circumcircle-tangent-congruent-angle-1.jpg) |
Geometry Problem 1431.
Triangle, Circumcircle, Parallel Chord, Apollonius, LLC, Congruent Angles, Poster, Conformal Mapping. |
![Problem 1430](../school-college/5/p1430-regular-octagon-area-1.jpg) |
Geometry Problem 1430. Regular Octagon, Area, Equivalent Figures,
Poster, Conformal Mapping. |
![Problem 1429](../school-college/5/p1429-triangle-median-angle-15-30-degree-1.jpg) |
Geometry Problem 1429. Triangle, Median, 15-30 degree, Angle, Congruence. |
![Problem 1428](../school-college/5/p1428-circle-tangent-triangle-square-area-1.jpg) |
Geometry Problem 1428. Intersecting Circles, Tangent Line, Triangle, Square, Area. |
![Problem 1427](../school-college/5/p1427-square-circle-tangent-radius-1.jpg) |
Geometry Problem 1427. Circle inscribed in a square, Arc, Tangent Line, Tangent Circles, Radii. |
![Problem 1426](../school-college/5/p1426-two-squares-triangle-quadrilateral-area-1.jpg) |
Geometry Problem 1426. Two Squares, Collinear Points, Triangle, Quadrilateral, Sum of the Areas. |
![Problem 1425](../school-college/5/p1425-two-squares-concurrent-lines-1.jpg) |
Geometry Problem 1425. Two Squares, Collinear Points, Concurrent Lines. |
![Problem 1424](../school-college/5/p1424-parallelogram-triangle-trapezoid-area-1.jpg) |
Geometry Problem 1424. Triangle, Parallelogram, Trapezoid, Area, Diagonal, Measurement. |
![Problem 1423](../school-college/5/p1423-triangle-equal-angle-similarity-area-1.jpg) |
Geometry Problem 1423. Triangle, Area, Three Equal Angles, Circumradius, Measurement. |
![Problem 1422](../school-college/5/p1422-triangle-cevian-transversal-area-1.jpg) |
Geometry Problem 1422. Triangle, Transversal, Cevian, Area, Measurement. |
![Problem 1421](../school-college/5/p1421-right-triangle-incircle-excircle-measurement-1.jpg) |
Geometry Problem 1421. Right Triangle, Incircle, Excircle, Tangent Lines, Measurement. |
![Problem 1420](../school-college/5/p1420-circle-area-regular-hexagon-tangent-1.jpg) |
Geometry Problem 1420. Regular Hexagon, Inscribed Circle, Area, Tangent
Circles, Tangent Line. |
![Problem 1419](../school-college/5/p1419-triangle-incenter-inradius-circumcircle-distance-sketch-ipad-1.jpg) |
Geometry Problem 1419. Triangle, Altitude, Circumcircle, Incenter, Inradius, Perpendicular, Angle Bisector, Midpoint. |
![Problem 1418](../school-college/5/p1418-triangle-incenter-parallel-angle-circle-tangent-1.jpg) |
Geometry Problem 1418. Triangle, Circumcircle, Incenter, Side, Sum of Segments, Tangent, Parallel, Angle. |
![Problem 1417](../school-college/5/p1417-triangle-incenter-circumcircle-tangent-cevian-bisector-perpendicular-1.jpg) |
Geometry Problem 1417. Triangle, Cevian, Circumcircle, Incenter, Perpendicular, Angle Bisector,
Tangent Lines, Tangent Circles. |
![Problem 1416](../school-college/5/p1416-right-triangle-altitude-incircle-excircle-tangent-45-degree-1.jpg) |
Geometry Problem 1416. Right Triangle, Altitude, Incircle, Excircle, Tangency Points, 45 Degree Angle. |
![Problem 1415](../school-college/5/p1415-right-triangle-altitude-incircle-excircle-tangent-isosceles-1.jpg) |
Geometry Problem 1415. Right Triangle, Altitude, Incircle, Excircle, Tangency Points, Isosceles Triangle. |
![Problem 1414](../school-college/5/p1414-right-triangle-altitude-incircle-excircle-tangent-isosceles-1.jpg) |
Geometry Problem 1414. Right Triangle, Altitude, Incircle, Excircle, Tangency Points, Isosceles Triangle. |
![Problem 1413](../school-college/5/p1413-right-triangle-incircle-excircle-tangent-isosceles-1.jpg) |
Geometry Problem 1413. Right Triangle, Incircle, Excircle, Tangency Points,
Isosceles Right Triangle. |
![Problem 1412](../school-college/5/p1412-right-triangle-incircle-excircle-tangent-45-degrees-1.jpg) |
Geometry Problem 1412. Right Triangle, Incircle, Excircle, Tangency Points,
45 Degree Angle. |
![Problem 1411](../school-college/5/p1411-right-triangle-incircle-excircle-tangent-isosceles-1.jpg) |
Geometry Problem 1411. Right Triangle, Incircle, Excircle, Tangency Points,
Isosceles Right Triangle. |
![Problem 1410](../school-college/5/p1410-right-triangle-incircle-excircle-tangent-45-degrees-1.jpg) |
Geometry Problem 1410. Right Triangle, Incircle, Excircle, Tangency Points,
45 Degree Angle. |
![Problem 1409](../school-college/5/p1409-right-triangle-incircle-excircle-tangent-collinear-1.jpg) |
Geometry Problem 1409. Right Triangle, Incircle, Excircle, Collinear Tangency Points, Collinearity. |
![Problem 1408](../school-college/5/p1408-right-triangle-incircle-excircle-midpoint-collinear-1.jpg) |
Geometry Problem 1408. Right Triangle, Incircle, Excircle, Incenter, Midpoint, Tangency Point, Collinearity. |
![Problem 1407](../school-college/5/p1407-right-triangle-incircle-excircle-collinearity-1.jpg) |
Geometry Problem 1407. Right Triangle, Incircle, Excircle, Collinear Tangency Points, Collinearity. |
![Problem 1406](../school-college/5/p1406-four-congruent-circles-measurement-tutor-1.jpg) |
Geometry Problem 1406. Four Congruent Circles, Measurement, Metric Relations,
Sum of the Squares. |
![Problem 1405](../school-college/5/p1405-four-congruent-circles-chords-tutor-1.jpg) |
Geometry Problem 1405. Four Congruent Circles, Congruent Chords. |
![Problem 1404](../school-college/5/p1404-three-circles-congruence-diameter-secant-collinear-tutor-1.jpg) |
Geometry Problem 1404. Three Circles, Center, Intersecting Points, Collinearity, Congruence. |
![Problem 1403](../school-college/5/p1403-quadrilateral-congruence-90-degree-angle-tutor-1.jpg) |
Geometry Problem 1403. Quadrilateral, 90 Degree Angle, Perpendicular, Congruence. |
![Problem 1402](../school-college/5/p1402-triangle-three-tangent-circles-diameter-collinearity-tutor-1.jpg) |
Geometry Problem 1402. Triangle, Three Tangent Circles, Parallel Diameter, Collinear Points. |
![Problem 1401](../school-college/5/p1401-rigth-triangle-isosceles-tangent-congruence-tutor-1.jpg) |
Geometry Problem 1401. Right Triangle with three circles on the sides, Isosceles, Diameter, Center, Tangent, Congruence. |
![Problem 1400](../school-college/4/p1400-triangle-rectangles-perpendicular-bisector-concurrency-1.jpg) |
Geometry Problem 1400. Triangle with three rectangles on the sides, Perpendicular Bisectors, Concurrency. |
![Problem 1399](../school-college/4/p1399-triangle-circumcircle-perpendicular-angle-congruence-1.jpg) |
Geometry Problem 1399.
Triangle, Circumcircle, Perpendiculars, Angles, Congruence, Cyclic Quadrilateral. |
![Problem 1398](../school-college/4/p1398-isosceles-triangle-circle-measurement-tutor-1.jpg) |
Geometry Problem 1398.
Isosceles Triangle, Circle, Radius, Perpendicular, Measurement. |
![Problem 1397](../school-college/4/p1397-circle-tangent-90-degree-collinear-tutoring-1.jpg) |
Geometry Problem 1397. Circle, Diameter, Tangent, Secant, 90 Degrees Angle,
Perpendicular, Collinear Points. |
![Problem 1396](../school-college/4/p1396-triangle-rectangles-perpendicular-concurrency-1.jpg) |
Geometry Problem 1396. Triangle with three rectangles on the sides, Vertices, Perpendicular lines, Concurrency. |
![Problem 1395](../school-college/4/p1395-triangle-rectangles-midpoints-concurrency-1.jpg) |
Geometry Problem 1395. Triangle with three rectangles on the sides, Midpoints, Perpendicular lines, Concurrency. |
![Problem 1394](../school-college/4/p1394-three-circles-common-internal-tangent-concurrent-1.jpg) |
Geometry Problem 1394. Three Circles and Three Pair of Common Internal Tangents, Concurrency. |
![Problem 1393](../school-college/4/p1393-monge-circle-theorem-tangent-collinear-tutor-1.jpg) |
Geometry Problem 1393. Monge's Circle Theorem, Three Circles and Three Pair of Common Tangents, Collinearity. |
![Problem 1392](../school-college/4/p1392-cyclic-quadrilateral-circle-tutor-1.jpg) |
Geometry Problem 1392. Two Cyclic Quadrilateral, Cyclic Octagon, Circle. |
![Problem 1391](../school-college/4/p1391-triangle-ratio-area-circumcircle-1.jpg) |
Geometry Problem 1391. Two Triangles, Ratio of Areas, Circumcircle. |
![Problem 1390](../school-college/4/p1390-triangle-point-perpendicular-sum-square-tutoring-1.jpg) |
Geometry Problem 1390. Triangle, any point, perpendicular, sum of the squares. |
![Problem 1389 40-120-20 triangle](../school-college/4/p1389-triangle-40-20-degree-angle-congruence-tutoring-1.jpg) |
Geometry Problem 1389. Triangle, 40-120-20 degree, Angle, Congruence. |
![Problem 1388 40-60-80 triangle](../school-college/4/p1388-triangle-40-60-80-degree-incenter-side-congruence-1.jpg) |
Geometry Problem 1388. Triangle 40-60-80 degree, Incenter, Congruence. |
![Problem 1387 Quadrilateral, Double Angle, Congruence, Isosceles Triangle](../school-college/4/p1387-quadrilateral-double-angle-isosceles-sum-tutoring-1.jpg) |
Geometry Problem 1387. Quadrilateral, Double Angle, Congruence, Isosceles Triangle. |
![Problem 1386 Thabit ibn Qurra Theorem,Pythagorean Theorem to any triangle](../school-college/4/p1386-triangle-thabit-ibn-qurra-similarity-pythagoras-1.jpg) |
Geometry Problem 1386. Thabit ibn Qurra (826 -901) Theorem and more conclusions, generalized Pythagorean Theorem to any triangle. |
![Problem 1385 Circle, Triangle](../school-college/4/p1385-triangle-circumcircle-orthocenter-bisector-collinear-1.jpg) |
Geometry Problem 1385. Triangle, Orthocenter, Circle, Circumcircle, Angle Bisector, Midpoint, Collinear Points. |
![Problem 1384 Circle, Triangle](../school-college/4/p1384-triangle-circumcircle-orthocenter-bisector-90-degree-1.jpg) |
Geometry Problem 1384. Triangle, Orthocenter, Circle, Circumcircle, Angle Bisector, 90 Degree. |
![Problem 1383 Circle, Triangle](../school-college/4/p1383-triangle-circle-midpoint-sum-product-secant-1.jpg) |
Geometry Problem 1383. Triangle, Median, Circle, Chord, Secant, Sum, Product. |
![Problem 1382 Circle, Diameter, Radius, Perpendicular, Congruence](../school-college/4/p1382-circle-diameter-perpendicular-congruence-tutoring-1.jpg) |
Geometry Problem 1382. Circle, Diameter, Radius, Perpendicular, Congruence. |
![Problem 1381 Parallelogram, Triangle, Area](../school-college/4/p1381-parallelogram-triangle-area-1.jpg) |
Geometry Problem 1381. Parallelogram, Exterior Point, Triangle, Area. |
![Problem 1380 Circles, Tangents, Chords](../school-college/4/p1380-two-circle-common-internal-tangent-congruent-chord-1.jpg) |
Geometry Problem 1380. Common
Internal Tangents. Circles, Secant, Congruent Chords. |
![Problem 1379 Circles, Tangents, Chords](../school-college/4/p1379-two-circle-common-external-tangent-congruent-chord-1.jpg) |
Geometry Problem 1379. Common External Tangents. Circles, Secant, Congruent Chords. |
![Problem 1378 Parallelogram](../school-college/4/p1378-parallelogram-diagonal-perpendicular-distance-1.jpg) |
Geometry Problem 1378. Parallelogram, Diagonal perpendicular to a side, Distances from a Point to Vertices, Measurement. |
![Problem 1377 Isosceles Triangle, Circle](../school-college/4/p1377-isosceles-triangle-interior-cevian-equal-sum-exradii-1.jpg) |
Geometry Problem 1377. Isosceles Triangle, Interior Cevian, Equal Sum of Exradii, Excircle. |
![Problem 1376 Isosceles Triangle, Circle](../school-college/4/p1376-isosceles-triangle-interior-cevian-exradius-parallel-1.jpg) |
Geometry Problem 1376. Isosceles Triangle, Interior Cevian, Excircles, Tangency Points, Parallel Lines. |
![Problem 1375 Isosceles Triangle, Circle](../school-college/4/p1375-isosceles-triangle-interior-cevian-exradius-altitude-1.jpg) |
Geometry Problem 1375. Isosceles Triangle, Interior Cevian, Exradius, Excircle, Altitude to the Base. |
![Problem 1374 Isosceles Triangle, Circle](../school-college/4/p1374-isosceles-triangle-exterior-cevian-incircle-excircle-parallel-1.jpg) |
Geometry Problem 1374. Isosceles Triangle, Exterior Cevian, Incircle, Excircle, Tangency Points, Parallel Lines. |
![Problem 1373 Isosceles Triangle, Altitude](../school-college/4/p1373-equilateral-triangle-interior-cevian-inradius-exradius-altitude-1.jpg) |
Geometry Problem 1373. Isosceles Triangle, Exterior Cevian, Inradius, Exradius, Altitude to the Base. |
![Problem 1372 Equilateral Triangle, Exterior Cevian, Inradius, Exradius, Altitude](../school-college/4/p1372-equilateral-triangle-exterior-cevian-inradius-exradius-altitude-1.jpg) |
Geometry Problem 1372. Equilateral Triangle, Exterior Cevian, Inradius, Exradius, Altitude, Sketch, iPad Apps. |
![Equilic Quadrilateral, problem 1371](../equilic/equilic_quadrilateral_05_1.jpg) |
Geometry Problem 1371: Equilic
Quadrilateral 5. |
![Equilic Quadrilateral, problem 1370](../equilic/equilic_quadrilateral_04_1.jpg) |
Geometry Problem 1370: Equilic
Quadrilateral 4 |
![Equilic Quadrilateral, problem 1369](../equilic/equilic_quadrilateral_03_1.jpg) |
Geometry Problem 1369: Equilic
Quadrilateral 3 |
![Equilic Quadrilateral, problem 1368](../equilic/equilic_quadrilateral_02_1.jpg) |
Geometry Problem 1368: Equilic
Quadrilateral 2 |
![Equilic Quadrilateral, problem 1367](../equilic/equilic_quadrilateral_01_1.jpg) |
Geometry Problem 1367: Equilic
Quadrilateral 1 |
![Geometry problem 1366](../school-college/4/p1366-square-perpendicular-angle-bisector-concylic-1.jpg) |
Geometry Problem 1366.
Square, Angle Bisector, Perpendicular, Concyclic Points, Circle, Sketch, iPad Apps. |
![Geometry problem 1365](../school-college/4/p1365-circle-chord-parallel-secant-tangent-midpoint-1.jpg) |
Geometry Problem 1365.
Circle, Tangent, Secant, Chord, Parallel, Midpoint, Sketch, iPad Apps. |
![Geometry problem 1364](../school-college/4/p1364-square-inscribed-circle-chord-pieces-area-1.jpg) |
Geometry Problem 1364.
Square, Inscribed Circle, Area, Angle Bisector, Perpendicular, 45 Degrees, Sketch, iPad Apps. |
![Geometry problem 1363](../school-college/4/p1363-square-perpendicular-angle-bisector-45-degree-1.jpg) |
Geometry Problem 1363.
Square, Angle Bisector, Perpendicular, 45 Degrees, Angle, Sketch, iPad Apps. |
![Geometry problem 1362](../school-college/4/p1362-equilateral-triangle-inscribed-circle-lunula-area-1.jpg) |
Geometry Problem 1362.
Equilateral Triangle Inscribed in a Circle, Lunula, Ratio of Areas, Tangent, Sketch, iPad Apps. |
![Geometry problem 1361](../school-college/4/p1361-two-nine-point-circle-angle-tutor-sketch-sw-1.jpg) |
Geometry Problem 1361.
Triangle, Two Nine-Point Circles, Feuerbach's Circle, Euler's Circle, Congruent Angles, Sketch, iPad Apps. |
![Geometry problem 1360](../school-college/4/p1360-nine-point-circle-euler-cyclic-tutor-sketch-sw-1.jpg) |
Geometry Problem 1360.
Triangle, Nine-Point Circle, Feuerbach's Circle, Euler's Circle, Cyclic Quadrilateral, Concyclic Points, Sketch, iPad Apps. |
![Geometry problem 1359](../school-college/4/p1359-triangle-circumcircle-equal-angle-midpoint-tutor-1.jpg) |
Geometry Problem 1359.
Triangle, Circumcircle, Congruent Angles, Midpoints. |
![Geometry problem 1358](../school-college/4/p1358-dodecagon-regular-concurrency-diagonal-infographic-classes-1.jpg) |
Geometry Problem 1358.
Regular Dodecagon, Diagonals, Concurrency, Points, Lines. |
![Geometry problem 1357](../school-college/4/p1357-dodecagon-regular-collinearity-infographic-classes-1.jpg) |
Geometry Problem 1357.
Regular Dodecagon, Diagonals, Concurrency, Collinearity, Points, Lines. |
![Geometry problem 1356](../school-college/4/p1356-triangle-30-degrees-angle-congruence-tutoring-1.jpg) |
Geometry Problem 1356.
Quadrilateral, Triangle, Angle, 30 Degrees, Congruence. |
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