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  2. Clock angle problem - Wikipedia

    en.wikipedia.org/wiki/Clock_angle_problem

    Clock angle problems relate two different measurements: angles and time. The angle is typically measured in degrees from the mark of number 12 clockwise. The time is usually based on a 12-hour clock. A method to solve such problems is to consider the rate of change of the angle in degrees per minute.

  3. Langley's Adventitious Angles - Wikipedia

    en.wikipedia.org/wiki/Langley's_Adventitious_Angles

    adventitious quadrangles problem. A quadrilateral such as BCEF is called an adventitious quadrangle when the angles between its diagonals and sides are all rational angles, angles that give rational numbers when measured in degrees or other units for which the whole circle is a rational number. Numerous adventitious quadrangles beyond the one ...

  4. Snell's law - Wikipedia

    en.wikipedia.org/wiki/Snell's_law

    As light passes the border between media, depending upon the relative refractive indices of the two media, the light will either be refracted to a lesser angle, or a greater one. These angles are measured with respect to the normal line, represented perpendicular to the boundary. In the case of light traveling from air into water, light would ...

  5. Intersecting chords theorem - Wikipedia

    en.wikipedia.org/wiki/Intersecting_chords_theorem

    In Euclidean geometry, the intersecting chords theorem, or just the chord theorem, is a statement that describes a relation of the four line segments created by two intersecting chords within a circle.

  6. Perpendicular - Wikipedia

    en.wikipedia.org/wiki/Perpendicular

    The segment AB is perpendicular to the segment CD because the two angles it creates (indicated in orange and blue) are each 90 degrees. The segment AB can be called the perpendicular from A to the segment CD, using "perpendicular" as a noun. The point B is called the foot of the perpendicular from A to segment CD, or simply, the foot of A on CD ...

  7. Solution of triangles - Wikipedia

    en.wikipedia.org/wiki/Solution_of_triangles

    To find an unknown angle, the law of cosines is safer than the law of sines. The reason is that the value of sine for the angle of the triangle does not uniquely determine this angle. For example, if sin β = 0.5, the angle β can equal either 30° or 150°. Using the law of cosines avoids this problem: within the interval from 0° to 180° the ...

  8. Tangent lines to circles - Wikipedia

    en.wikipedia.org/wiki/Tangent_lines_to_circles

    The radius of a circle is perpendicular to the tangent line through its endpoint on the circle's circumference. Conversely, the perpendicular to a radius through the same endpoint is a tangent line. The resulting geometrical figure of circle and tangent line has a reflection symmetry about the axis of the radius.

  9. Carnot's theorem (perpendiculars) - Wikipedia

    en.wikipedia.org/wiki/Carnot's_theorem...

    Carnot's theorem: if three perpendiculars on triangle sides intersect in a common point F, then blue area = red area. Carnot's theorem (named after Lazare Carnot) describes a necessary and sufficient condition for three lines that are perpendicular to the (extended) sides of a triangle having a common point of intersection.

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