Area of a circle "ds" over the whole circle formula_33 is just the arc length, which is its circumference, so this shows that the area "A" enclosed by the circle is equal to formula_34 times the circumference of the circle. Note that the area of a semicircle of radius r can be computed by the integral formula_35. By trigonometric substitution, we substitute formula_36, hence formula_37 The last step follows since the trigonometric identity formula_42 implies that formula_43 and formula_44 have equal integrals over the interval formula_45, using integration by substitution. But on the other hand, since formula_46, the sum of the two integrals is
Distance from a point to a line to the point P. Hence: We can solve this equation for "x", The y coordinate of the point of intersection can be found by substituting this value of "x" into the equation of the original line, Using the equation for finding the distance between 2 points, formula_35, we can deduce that the formula to find the shortest distance between a line and a point is the following: Recalling that "m" = -"a"/"b" and "k" = - "c"/"b" for the line with equation "ax" + "by" + c = 0, a little algebraic simplification reduces this to the standard expression. The