Tangent Lines

Front

What is a tangent line?

Back

A tangent line is a straight line that touches a curve at a single point without crossing it.

Front

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

Back

You can determine if a line is tangent to a circle by using the Pythagorean Theorem. If the distance from the center of the circle to the line equals the radius, the line is tangent.

Front

What is the Pythagorean Theorem?

Back

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

Front

If a tangent line is drawn to a circle, what is the relationship between the radius and the tangent line at the point of contact?

Back

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

Front

What is the formula to 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 formula: length = √(d² - r²), where d is the distance from the point to the center of the circle and r is the radius.

Front

How do you find the value of x in a right triangle using the Pythagorean Theorem?

Back

To find x, rearrange the Pythagorean Theorem: x = √(a² + b²) if x is the hypotenuse, or x = √(c² - a²) or x = √(c² - b²) if x is one of the legs.

Front

What does it mean for a line to be 'assumed tangent'?

Back

Assuming a line is tangent means that you consider it tangent based on visual evidence or given information, even if it hasn't been mathematically verified.

Front

In a circle, if the radius is 5 units, what is the distance from the center to a tangent line?

Back

The distance from the center to the tangent line must also be 5 units for the line to be tangent.

Front

What is the significance of the point of tangency?

Back

The point of tangency is the exact point where the tangent line touches the curve, and it is the only point of contact.

Front

If a tangent line intersects a radius at a right angle, what can be concluded?

Back

It can be concluded that the line is indeed a tangent line to the circle.