College

Thank you for visiting I True or False Write TRUE if the statement is correct and FALSE if the statement is incorrect 1 A line coplanar with the circle. This page is designed to guide you through key points and clear explanations related to the topic at hand. We aim to make your learning experience smooth, insightful, and informative. Dive in and discover the answers you're looking for!

I. True or False. Write TRUE if the statement is correct and FALSE if the statement is incorrect.

1. A line coplanar with the circle and intersects it in one and only one point is tangent to a circle. ________

2. An external secant segment is a part of a secant segment that is inside a circle. ________

3. When a secant and a tangent intersect at the point of tangency, the measure of each angle formed is one-half the measure of its intercepted arc. ________

4. A sector of a circle is the region bounded by an arc of the circle and the two radii to the endpoints of the arc. ________

5. If two tangents intersect in the interior of a circle, the measure of an angle formed is one-half the sum of the measures of the arcs intercepted by the angle and its vertical angle. ________

6. If a line is perpendicular to a radius of a circle at its endpoint that is on the circle, then the line is tangent to the circle. ________

7. If two secants intersect in the exterior of a circle, then the measure of the angle formed is one-half the positive difference of the measures of the intercepted arcs. ________

Answer :

Final answer:

1. True. A tangent line intersects a circle at one point. 2. False. An external secant segment is outside the circle. 3. True. Angle formed by a secant and tangent are half the measure of the intercepted arc. 4. True. A sector is the region bounded by an arc and radii. 5. False. Measure of angle formed by intersecting tangents is half the difference of the intercepted arcs. 6. True. Perpendicular line to a radius is a tangent. 7. False. Measure of angle formed by two secants intersecting in the exterior is half the sum of the intercepted arcs.

Explanation:

1. True. A line that is coplanar with a circle and intersects it in one and only one point is tangent to the circle. This is because a tangent line touches the circle at only one point.

2. False. An external secant segment is a part of a secant segment that is outside the circle, not inside.

3. True. When a secant and a tangent intersect at the point of tangency, the measure of each angle formed is one-half the measure of its intercepted arc. This is known as the Angle-Tangent Theorem.

4. True. A sector of a circle is the region bounded by an arc of the circle and the two radii to the endpoints of the arc.

5. False. If two tangents intersect in the interior of a circle, the measure of the angle formed is one-half the difference of the measures of the arcs intercepted by the angle and its vertical angle, not the sum.

6. True. If a line is perpendicular to a radius of a circle at its endpoint that is on the circle, then the line is tangent to the circle. This is because a tangent line is perpendicular to the radius at the point of tangency.

7. False. If two secants intersect in the exterior of a circle, then the measure of the angle formed is one-half the sum of the measures of the intercepted arcs, not the positive difference.

Thank you for reading the article I True or False Write TRUE if the statement is correct and FALSE if the statement is incorrect 1 A line coplanar with the circle. We hope the information provided is useful and helps you understand this topic better. Feel free to explore more helpful content on our website!

Rewritten by : Jeany

Other Questions