Tangent Lines of Circles

Front

What is a tangent line to a circle?

Back

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

Front

If a line is tangent to a circle, then it is ________ to the radius drawn to the point of tangency.

Back

perpendicular

Front

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

Back

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

Front

Given a point B is 17cm away from the center O of a circle and AB is the tangent to the circle at A, if AB = 15 cm, find the radius of the circle.

Back

8 cm

Front

What is the formula to find the radius of a circle when given the distance from the center to a point outside the circle and the length of the tangent?

Back

Using the Pythagorean theorem: r = √(d² - t²), where d is the distance from the center to the external point and t is the length of the tangent.

Front

Determine if a tangent line is shown in the picture: (insert image).

Back

No

Front

What is the definition of a circle?

Back

A circle is a set of points in a plane that are equidistant from a fixed point called the center.

Front

What is the point of tangency?

Back

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

Front

How can you identify a tangent line in a diagram?

Back

A tangent line will touch the circle at only one point and will not cross into the circle.

Front

What is the significance of the radius in relation to tangent lines?

Back

The radius at the point of tangency is crucial for determining the angle and relationship between the tangent and the circle.