Geometry Problems 1411-1420. Level: High School, College

Geometry Problems 1411 - 1420

Geometry Problem 1411.
Right Triangle, Incircle, Excircle, Tangency Points, Isosceles Right Triangle.

Geometry Problem 1412.
Right Triangle, Incircle, Excircle, Tangency Points, 45 Degree Angle.

Geometry Problem 1413.
Right Triangle, Incircle, Excircle, Tangency Points, Isosceles Right Triangle.

Geometry Problem 1414.
Right Triangle, Altitude, Incircle, Excircle, Tangency Points, Isosceles Triangle.

Geometry Problem 1415.
Right Triangle, Altitude, Incircle, Excircle, Tangency Points, Isosceles Triangle.

Geometry Problem 1416.
Right Triangle, Altitude, Incircle, Excircle, Tangency Points, 45 Degree Angle.

Geometry Problem 1417.
Triangle, Cevian, Circumcircle, Incenter, Perpendicular, Angle Bisector, Tangent Lines, Tangent Circles.

Geometry Problem 1418.
Triangle, Circumcircle, Incenter, Side, Sum of Segments, Tangent, Parallel, Angle.

Geometry Problem 1419.
Triangle, Altitude, Circumcircle, Incenter, Inradius, Perpendicular, Angle Bisector, Midpoint.

Geometry Problem 1420.
Regular Hexagon, Inscribed Circle, Area, Tangent Circles, Tangent Line.

Geometry Problem 1421.
Right Triangle, Incircle, Excircle, Tangent Lines, Measurement.

Geometry Problem 1422.
Triangle, Transversal, Cevian, Area, Measurement.

Geometry Problem 1423.
Triangle, Area, Three Equal Angles, Circumradius, Measurement.

Geometry Problem 1424.
Triangle, Parallelogram, Trapezoid, Area, Diagonal, Measurement.

Geometry Problem 1425.
Two Squares, Collinear Points, Concurrent Lines.

Geometry Problem 1426.
Two Squares, Collinear Points, Triangle, Quadrilateral, Sum of the Areas.

Geometry Problem 1427.
Circle inscribed in a square, Arc, Tangent Line, Tangent Circles, Radii.

Geometry Problem 1428.
Intersecting Circles, Tangent Line, Triangle, Square, Area.

Geometry Problem 1429.
Triangle, Median, 15-30 degree, Angle, Congruence.

Geometry Problem 1430.
Regular Octagon, Area, Equivalent Figures, Poster, Conformal Mapping.

Geometry Problem 1431.
Triangle, Circumcircle, Parallel Chord, Apollonius, LLC, Congruent Angles, Poster, Conformal Mapping.

Geometry Problem 1432.
Tangent Circles, Secant, Tangent Lines, Proportionality, Similarity.

Geometry Problem 1433.
Tangent Circles, Diameter, Perpendicular, Midpoint, Measurement, Poster Typography, iPad Apps.

Geometry Problem 1434.
Equilateral Triangle, Tangent Circles, Tangent Lines, Arithmetic Mean, Measurement, Poster, Typography, iPad Apps.

Geometry Problem 1435.
Circle, Diameter, Inscribed Circles, Circular Sector, Parallelogram, Parallel Lines, Tangency Points, Poster, Typography, iPad Apps.

Geometry Problem 1436.
Right Triangle, Altitude, Excircles, Excenters, Geometric Mean, Measurement, Art, Poster, Typography, iPad Apps.

Geometry Problem 1437.
Intersecting Circles, Common Tangent, Equal Product, Art, Poster, Typography, iPad Apps.

Geometry Problem 1439.
Rectangle, Diagonal, Perpendicular, Circles, Areas, Art, Poster, Typography, iPad Apps.

Geometry Problem 1440.
Intersecting Circles, Perpendicular Bisector, Collinear Points, Art, Poster, Typography, iPad Apps.

Geometry Problem 1441.
Intersecting Circles, Perpendicular Bisector, Parallel Lines, Art, Poster, Typography, iPad Apps.

Geometry Problem 1442.
Triangle, Altitudes, Orthocenter, Perpendicular, Congruent Angles, Similarity, Measurement, Art, Poster, Typography, iPad Apps.

Geometry Problem 1443.
Triangle Area, Incenter, Circumcenter, 90 Degree, Perpendicular, One-third Area, Art, Poster, Typography, iPad Apps.

Dynamic Geometry Problem 1444.
The Asymmetric Propeller Theorem, Equilateral Triangles, Midpoints. Using GeoGebra.

Dynamic Geometry Problem 1445.
Van Aubel's theorem, Quadrilateral and Four Squares, Centers. Step-by-step animation using GeoGebra.

Dynamic Geometry Problem 1446.
Lemoine Line, triangle, circumcircle, tangent, collinear points. Step-by-step animation using GeoGebra.

Dynamic Geometry Problem 1447.
Outer Vecten Point. Step-by-step illustration using GeoGebra.

Dynamic Geometry 1448.
Simson Line. Step-by-step illustration using GeoGebra.

Dynamic Geometry 1449.
Salmon Line. Step-by-step illustration using GeoGebra.

Dynamic Geometry 1450.
Ortholine, Steiner Line, Complete Quadrilateral, Collineal Orthocenters. Step-by-step illustration using GeoGebra.

Dynamic Geometry 1451.
Orthopole of a Line. Step-by-step illustration using GeoGebra.

Dynamic Geometry 1452.
Japanese Theorem, Sangaku, Cyclic Quadrilateral, Incenter, Rectangle, Inradius. Step-by-step illustration using GeoGebra.

Geometry Problem 1453.
Two Semicircles, Cyclic Quadrilateral, Concyclic Points, iPad.

Geometry Problem 1454.
Intersecting Circles, Perpendicular Lines, Cyclic Quadrilateral, Collinear Points, iPad. Step-by-step illustration using GeoGebra.

Geometry Problem 1455.
Nagel Point, Excircles, Incircle, Congruent Segments, iPad. Step-by-step illustration using GeoGebra.

Geometry Problem 1456.
Altitudes, Orthic Triangle, Circumcircle, Parallel lines, Similarity, Area, iPad. Step-by-step illustration using GeoGebra.

Geometry Problem 1457.
Altitudes, Circles, Similarity, Product of the Inradii Lengths, iPad. Step-by-step illustration using GeoGebra.

Geometry Problem 1458.
Triangle, Incircles, Excircle, Area, Step-by-step Illustration using GeoGebra.

Geometry Problem 1459.
Two Triangles, Orthocenter, Midpoint, Perpendicular, Step-by-step Illustration using GeoGebra.

Dynamic Geometry 1460.
Newton-Gauss Line, Complete Quadrilateral, Midpoints of Diagonals, Collinear Points, Step-by-step Illustration using GeoGebra.

Geometry Problem 1461.
Quadrilateral, Triangle, Angles, 30-60 Degree, Congruence, Auxiliary Lines.

Geometry Problem 1461.
Quadrilateral, Triangle, Angles, 30-60 Degree, Congruence, Auxiliary Lines.

Geometry Problem 1462.
Newton-Line, Newton-Gauss Line, Complete Quadrilateral, Midpoints of Sides and Diagonals, Collinear Points. Step-by-step Illustration using GeoGebra.

Geometry Problem 1463.
Parallelogram, Interior Point, Opposite Triangles with Equal Sum of Areas. Step-by-step Illustration using GeoGebra.

Geometry Problem 1464.
Quadrilateral, Interior Point, Midpoint of Sides, Equal Sum of Areas. Step-by-step Illustration using GeoGebra.

Geometry Problem 1465.
Tangential Quadrilateral, Incenter, Inscribed Circle, Equal Sum of Areas. Step-by-step Illustration using GeoGebra.

Geometry Problem 1466.
Tangential Quadrilateral, Newton Line, Incenter, Midpoint, Diagonal, Collinear Points. Step-by-step Illustration using GeoGebra.

Geometry Problem 1467.
Square, Rectangle, Triangle, Area.

Dynamic Geometry 1468.
Steiner's Theorem, Triangle, Circumradius, Inradius, Sum of Exradii, Step-by-step Illustration.

Dynamic Geometry 1469.
Triangle, Circumradius, Inradius, Midpoints, Arcs, Sum of Distances, Step-by-step Illustration.

Dynamic Geometry 1470.
Tangential Quadrilateral, Incircles, Tangent, Parallel, Rhombus, Step-by-step Illustration.

Dynamic Geometry 1471.
Equilateral Triangle, Inside/Outside Point, Incenters, Tangency Points, Concurrent Lines, Step-by-step Illustration.

Dynamic Geometry 1472.
Cyclic Quadrilateral, Perpendicular Diagonals, Rectangle, Step-by-step Illustration.

Dynamic Geometry 1473.
Kosnita's Theorem, Triangle, Four Circumcenters, Concurrent Line, Step-by-step Illustration.

Dynamic Geometry 1474.
Butterfly Theorem, Circle, Chords, Midpoints, Step-by-step Illustration.

Dynamic Geometry 1475.
Clifford Intersecting Circles Theorem, Step-by-step Illustration, GeoGebra, iPad.

Dynamic Geometry 1476.
Droz-Farny Line Theorem, Triangle, Orthocenter, Perpendicular, Collinear Midpoints, Step-by-step Illustration. GeoGebra, iPad.

Dynamic Geometry 1477.
Miquel's Pentagram Theorem, Pentagon, Triangle, Circumcircles, Concyclic Points, Step-by-step Illustration. GeoGebra, iPad.

Dynamic Geometry 1479.
Triangle, Circumcircle, Angle Bisector, Perpendicular Bisector, Chord, Concyclic Points, Parallel Lines,, Step-by-step Illustration. GeoGebra, iPad.

Dynamic Geometry 1479.
Triangle, Circumcircle, Angle Bisector, Perpendicular Bisector, Chord, Concyclic Points, Parallel Lines,, Step-by-step Illustration. GeoGebra, iPad.

Dynamic Geometry 1480.
Japanese Theorem for Cyclic Polygon, Triangulation, Non-intersecting Diagonals, Sum of Inradii, Invariant, Step-by-step Illustration. GeoGebra, iPad.

Dynamic Geometry 1481.
Five Tangential or Circumscribed Quadrilaterals, Pitot Theorem, Congruence, Step-by-step Illustration. GeoGebra, iPad.

Geometry Problem 1482.
Right Triangle, Perpendicular, Double Angle, Measurement.

Geometry Problem 1483.
Isosceles Right Triangle, Excenter, Perpendicular, Measurement.

Geometry Problem 1484.
Right Triangle, Altitude, Incircles, Inradius, Measurement.

Geometry Problem 1485.
Triangle, Orthocenter, Altitude, Circle, Diameter, Tangent, Measurement.

Geometry Problem 1486.
Right Triangle, Altitude, Incircle, Tangent, Measurement.

Geometry Problem 1487.
Right Triangle, Altitude, Incircle, Tangent, Measurement.

Geometry Problem 1488.
Right Triangle, Altitude, Incircle, Tangent, Measurement.

Geometry Problem 1489.
Right Triangle, Angle Bisectors, Perpendicular, Measurement.

Geometry Problem 1490.
Triangle, Cevian, Incircle, Tangent, Measurement.

Geometry Problem 1491.
Cyclic Quadrilateral, Diagonal, Incircle, Angle, Measurement.

Geometry Problem 1492.
Right Triangle, Altitude, Incenters, Angle, Measurement.

Geometry Problem 1493.
Four Squares, Parallelogram, Auxiliary Lines.

Geometry Problem 1494.
Parallelogram, Midpoints, Octagon, Areas.

Geometry Problem 1498.
Intersecting Circles, Diameter, Common Chord, Secant, Cyclic Quadrilateral, Concurrent Lines, Concyclic and Collinear Points.

Geometry Problem 1499.
Triangle, Angles, Cevian, Congruence, Isosceles, Equilateral, Auxiliary Construction.

Geometry Problem 1500.
Circle, Perpendicular, Tangent, Secant, Cyclic Quadrilateral, Parallel, Similarity, Measurement.

Geometry Problem 1501.
Square, Exterior Point, Congruent Angles, Segment, Measurement.

Geometry Problem 1502.
Right Triangle, Incircle, Inradius, Geometric Mean of 2 Inradii, Angle Bisector, Perpendicular, Tangential Quadrilateral.

Geometry Problem 1503.
Triangle, Incircle, Tangent, Congruence, Perpendicular.

Geometry Problem 1504.
Squares, Equilateral Triangle, Parallel, Angle.

Geometry Problem 1505.
Parallel Rays, Angles, and Bisector, Corresponding, Alternate, Conjugate.

Geometry Problem 1506.
Parallel Rays, Angles, Corresponding, Alternate.

Geometry Problem 1507.
Understanding Triangle Geometry: Double Angles, Altitudes, and Measurements. Difficulty Level: High School.

Geometry Problem 1508.
Understanding Triangle Geometry: Isosceles, Equilateral, Quadrilateral, Angular. Difficulty Level: High School.

Geometry Problem 1509 and Poem.
Congruence of Triangles in a Trapezoid and a Square, Measurement. Difficulty Level: High School.

Geometry Problem 1510 and Poem.
Congruence of Triangles, Perimeter, Measurement. Difficulty Level: High School.

Geometry Problem 1511 and Poem.
Finding the Altitude of an Isosceles Triangle Using Distances from a Point on the Extension of the Base. Difficulty Level: High School.

Geometry Problem 1512 and a Thematic Poem.
Finding the Length of a Segment in a Triangle with a Median and a Cevian with Given Ratio. Difficulty Level: High School.

Geometry Problem 1513 and a Thematic Poem.
Solving the base in a Right Trapezoid with Double Angle and Sum of Two Sides. Difficulty Level: High School.

Geometry Problem 1514 and a Thematic Poem.
Discover the Secret to Finding Distances in Regular Hexagons with Interior Squares. Difficulty Level: High School.

Geometry Problem 1515 and a Thematic Poem.
Mastering Triangle Distance Calculation: Find the Distance from the Intersection of Medians to an Exterior Line. Difficulty Level: High School.

Geometry Problem 1516 and a Thematic Poem.
Finding the Length of a Side in an Equiangular Hexagon with Given Three Side Lengths. Difficulty Level: High School.

Geometry Problem 1517 and a Thematic Poem.
Unlocking Triangle Side Length: Solving with a Median and Two Angles. Difficulty Level: High School.