Tangent Segments to a Circle - Problem 3

To find the measure of an arc between two points of tangency, first recall that the measure of an arc is the same as the measure of the central angle whose legs intersect the circle at the points where the arc begins and ends. Also recall that the tangent lines drawn from a point outside the circle form two congruent segments. In addition, a radius intersects a point of tangency at a right angle. As a result, a quadrilateral is formed with the two tangent lines and radii. Since the measure of the angle formed by the tangent lines is known, and the the two right angles formed by the radii and tangent lines are known, the missing angle is the measure of the central angle. To solve for this central angle, subtract the known angles from 360°, since the sum of the angles in a quadrilateral is always 360°. Since this central angle is the same as the measure of the arc, you have found the measure of the intercepted arc formed by the two tangent lines.