Tangents and circles

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 a tangent line intersects a circle, how many points does it touch?

Back

A tangent line intersects a circle at exactly one point.

Front

What is the formula for finding 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: \( t = \sqrt{d^2 - r^2} \), where \( t \) is the tangent length, \( d \) is the distance from the external point to the center of the circle, and \( r \) is the radius.

Front

If QS is a tangent to circle P and the radius is 12, what is the length of QS?

Back

12

Front

How do you find the missing side of a right triangle formed by a radius and a tangent?

Back

Use the Pythagorean theorem: \( a^2 + b^2 = c^2 \), where \( c \) is the hypotenuse (the radius), and \( a \) and \( b \) are the lengths of the tangent and the segment from the center to the point of tangency.

Front

What is the value of x if a tangent segment and a secant segment are involved?

Back

Use the tangent-secant theorem: \( t^2 = p(p + s) \), where \( t \) is the tangent segment, \( p \) is the external part of the secant, and \( s \) is the internal part.

Front

What is the definition of a secant line?

Back

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

Front

What is the difference between a tangent and a secant?

Back

A tangent touches the circle at one point, while a secant intersects the circle at two points.

Front

How can you determine if two segments are tangent to a circle?

Back

If the segments are equal in length and both touch the circle at one point, they are tangent.