Tangents of a Circle

Front

What is a tangent to a circle?

Back

A tangent to a circle is a straight line that touches the circle at exactly one point, known as the point of tangency.

Front

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

Back

The radius drawn to the point of tangency is perpendicular to the tangent line.

Front

How do you find the length of a tangent segment from a point outside the circle?

Back

The length of the tangent segment can be found using the Pythagorean theorem, where the tangent segment, the radius, and the distance from the point to the center of the circle form a right triangle.

Front

What is the Pythagorean theorem?

Back

The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides (a² + b² = c²).

Front

If two tangent segments are drawn from a single external point to a circle, what can be said about their lengths?

Back

The lengths of the two tangent segments are equal.

Front

What is the formula for the length of a tangent segment from a point outside the circle?

Back

If 'd' is the distance from the external point to the center of the circle and 'r' is the radius, the length of the tangent segment 't' can be calculated as t = √(d² - r²).

Front

How do you identify the point of tangency in a diagram?

Back

The point of tangency is where the tangent line touches the circle, and it is often marked or can be identified by the right angle formed with the radius.

Front

What is the significance of the right triangle formed by a tangent and a radius?

Back

The right triangle formed by a tangent and a radius allows the use of trigonometric ratios and the Pythagorean theorem to solve for unknown lengths.

Front

What is the definition of a secant line?

Back

A secant line is a line that intersects a circle at two points.

Front

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

Back

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