What is the measure of the angle formed by two tangents drawn to a circle from an external point if they intersect a major arc whose measure is 230?

Answer 1

-- The major arc = 230 degrees

-- The minor arc ... the arc between the tangents ... is (360 - 230) = 130 degrees.

-- The line from the vertex of the angle to the center of the circle bisects the arc,

so the angle between that line and the radius to each tangent is 65 degrees.

-- The radius to each tangent is perpendicular to the tangent. So the radius, the tangent,

and the line from the vertex to the center of the circle is a right triangle.

-- In the right triangle, there's 90 degrees where the radius meets the tangent, and

65 degrees at the center of the circle. That leaves 25 degrees for the angle at the

vertex.

-- With another 25 degrees for the right triangle formed by the other tangent,

the total angle formed by the two tangents is 50 degrees.