Tangents of Circles

How do you find the radius of a circle when given the length of a tangent and the distance from the center to the point of tangency?

• Use the formula: radius^2 + tangent_length^2 = distance_from_center^2.

• Multiply the tangent length by 2 to get the radius.

• Add the tangent length to the distance from the center to get the radius.

• Subtract the tangent length from the distance from the center to get the radius.

If a line segment AB is tangent to circle C at point A, what can be said about the distance from the center of the circle to point A?

• The distance from the center of the circle to point A is the diameter of the circle.

• The distance from the center of the circle to point A is the radius of the circle.

• The distance from the center of the circle to point A is twice the radius of the circle.

• The distance from the center of the circle to point A is equal to the circumference of the circle.

What is the relationship between two tangents drawn from the same external point to a circle?

• The lengths of the two tangents drawn from the same external point to a circle are equal.

• The angles between the tangents and the radius are always 90 degrees.

• The tangents intersect at the center of the circle.

• The lengths of the tangents are always different.

If a tangent line is drawn to a circle, what can be said about the angles formed with the radius?

• The angle formed between the tangent line and the radius at the point of tangency is 90 degrees.

• The angle formed between the tangent line and the radius is always acute.

• The angle formed between the tangent line and the radius is always obtuse.

• The angle formed between the tangent line and the radius is equal to the angle subtended by the diameter.

What is the definition of a secant line in relation to a circle?

• A line that touches a circle at one point.

• A line that intersects a circle at two points.

• A line that is tangent to the circle.

• A line that is parallel to the radius of the circle.

If the radius of a circle is 10 cm, what is the length of a tangent from a point 15 cm away from the center?

• 8.00 cm

• 9.00 cm

• 11.18 cm

• 12.00 cm

What is the importance of understanding tangents in geometry?

• Understanding tangents is crucial for solving problems related to circles, angles, and distances in geometry.

• Tangents are only relevant in calculus and have no importance in geometry.

• Tangents help in calculating the area of triangles and rectangles.

• Understanding tangents is essential for solving problems related to polygons.

How can you determine if a line is a tangent to a circle?

• A line is a tangent to a circle if it touches the circle at exactly one point and is perpendicular to the radius at that point.

• A line is a tangent to a circle if it intersects the circle at two points.

• A line is a tangent to a circle if it is parallel to the diameter of the circle.

• A line is a tangent to a circle if it passes through the center of the circle.

What is the relationship between a tangent and the radius at the point of tangency?

• A tangent is parallel to the radius drawn to the point of tangency.

• A tangent is perpendicular to the radius drawn to the point of tangency.

• A tangent bisects the radius at the point of tangency.

• A tangent is equal in length to the radius at the point of tangency.

What is a tangent to a circle?

• A line that intersects the circle at two points.

• A straight line that touches the circle at exactly one point.

• A line that passes through the center of the circle.

• A line that is parallel to the radius of the circle.