Tangent Lines

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

How can you determine if a line is tangent to a circle using the Pythagorean Theorem?

Back

If the distance from the center of the circle to the line is equal to the radius, then the line is tangent to the circle.

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

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

Using the formula: length = √(13² - 5²) = √(169 - 25) = √144 = 12 units.

Front

What is the definition of a circumscribed polygon?

Back

A circumscribed polygon is a polygon whose sides are tangent to a circle.

Front

How do you find the perimeter of a circumscribed polygon if the radius of the inscribed circle is known?

Back

The perimeter can be found by multiplying the number of sides by the length of one side, which can be determined using the radius and the angles of the polygon.

Front

What is the significance of the point of tangency in relation to the circle?

Back

The point of tangency is the only point where the tangent line touches the circle, and it is crucial for determining angles and distances related 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 of the circle.

Front

If a tangent line intersects a circle at point A and a chord intersects at point B, what can be said about the angles ∠TAB and ∠C?

Back

∠TAB is equal to the angle ∠C formed by the chord at the opposite side of the circle.