Is it true or false that the measure of a tangent-chord angle is twice the measure of the intercepted arc inside the angle?

Answer 1

It is true that the measure of a tangent-chord angle is half the measure of the intercepted arc inside the angle.

When a tangent line intersects a chord of a circle, it creates an angle between the tangent line and the chord, known as the tangent-chord angle. If we draw a segment from the center of the circle to the midpoint of the chord, it will bisect the chord, and the tangent-chord angle will be formed by two smaller angles, one at each end of this segment.

Now, the intercepted arc inside the tangent-chord angle is the arc that lies between the endpoints of the chord and is inside the angle. The measure of this arc is half the measure of the central angle that subtends the same arc, which is equal to the measure of the angle formed by the two smaller angles at the ends of the segment that bisects the chord.

Therefore, we can conclude that the measure of a tangent-chord angle is half the measure of the intercepted arc inside the angle.

Answer 2

false