# Through A Rational Point On A Unit Circle

Pythagorean triples {a, b, c} will give rational points (a/c, b/c) on a unit circle.

Select a rational point, (a/c, b/c), on the unit circle then write the equation of the line through this point and the origin, (0, 0). The radius of the circle is on this line.

Write the equation of the line through (a/c, b/c) that is perpendicular to the radius.

This time use the slope intercept form for your answer and keep the numbers in ratio form rather than decimal form. An example is given in the graph above where y = (-24/7)x + ( 25/7) is tangent to this first quadrant arc of a unit circle and perpendicular to the radial line y = ( 7/24)x. A "pythagoperp" line is a line that pass through a rational point on a unit circle and is perpendicular to a radial line at that rational point. A pythagoperp line is tangent to a unit circle at the rational point of tangency.

Pythagorean Triples Points on a unit circle.
Finding Pythagorean Triples Lines through a unit circle.
Pythagorean Triples overlap parts 3, 4 and 5
Pythagorean Triples Indexed Into Series
Problems for math classes