Unit 10: Circles Homework 5: Tangent Lines Flashcard

Front

What is a tangent line?

Back

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

Front

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

Back

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

Front

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

Back

The lengths of the two tangent segments are equal.

Front

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

Back

Use the Pythagorean theorem: if the distance from the point to the center of the circle is 'd' and the radius is 'r', then the length of the tangent segment 't' is given by t = √(d² - r²).

Front

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

Back

Length of tangent segment = √(distance from point to center² - radius²).

Front

If a tangent line intersects a radius at a right angle, what does this imply about the tangent line?

Back

It confirms that the line is indeed a tangent line to the circle.

Front

What is the significance of the point of tangency?

Back

The point of tangency is the only point where the tangent line touches the circle.

Front

How can you determine if a line is tangent to a circle using the distance from the center?

Back

If the distance from the center to the line equals the radius, the line is tangent to the circle.

Front

What is the relationship between the angles formed by a tangent and a chord through the point of tangency?

Back

The angle formed between the tangent and the chord is equal to the angle in the alternate segment.

Front

If a circle has a radius of 5 units, what is the length of a tangent segment from a point 13 units away from the center?

Back

Length of tangent segment = √(13² - 5²) = √(169 - 25) = √144 = 12 units.