Lines Tangent to Circles Mini Flashcard #2

Front

What is a tangent line to a circle?

Back

A tangent line 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 line 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 the hypotenuse in a right triangle formed by a tangent and a radius?

Back

Use the Pythagorean theorem: c² = a² + b², where c is the hypotenuse, and a and b are the lengths of the other two sides.

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): c² = a² + b².

Front

If a tangent line and a radius form a right triangle, what can you conclude about the angles?

Back

The angle between the radius and the tangent line at the point of tangency is 90 degrees.

Front

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

Back

The length of the tangent segment can be found using the formula: length = √(d² - r²), where d is the distance from the external point to the center of the circle, and r is the radius.

Front

How do you determine if two lines are tangent to a circle?

Back

Two lines are tangent to a circle if they touch the circle at exactly one point each and do not cross the circle.

Front

What is the significance of the center of the circle (O) in tangent problems?

Back

The center of the circle (O) is crucial for determining distances, angles, and relationships between the radius and tangent lines.

Front

What is the definition of a right triangle?

Back

A right triangle is a triangle that has one angle measuring 90 degrees.

Front

How can you apply the properties of tangents and circles to solve for unknown lengths?

Back

Use the relationships between the tangent, radius, and the Pythagorean theorem to set up equations that can be solved for unknown lengths.