6.3/6.4 Special Segments in Circles

Front

What is a tangent to a circle?

Back

A tangent to a circle is a straight line that touches the circle at exactly one point.

Front

What is the relationship between a radius and a tangent at the point of contact?

Back

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

Front

Define a secant line in relation to a circle.

Back

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

Front

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

Back

The length of the tangent segment is given by the formula: \( t = \sqrt{d^2 - r^2} \), where \( d \) is the distance from the point to the center of the circle and \( r \) is the radius.

Front

What is the measure of an angle formed by two tangents drawn from a point outside the circle?

Back

The measure of the angle formed by two tangents is equal to half the difference of the measures of the intercepted arcs.

Front

How do you find the length of a tangent segment if you know the radius and the distance from the external point to the center?

Back

Use the formula: \( t = \sqrt{d^2 - r^2} \) to calculate the length of the tangent segment.

Front

What is the power of a point theorem?

Back

The power of a point theorem states that for any point outside a circle, the square of the length of the tangent segment from the point to the circle is equal to the product of the lengths of the segments of any secant line drawn from that point.

Front

If two tangents are drawn from a point outside a circle, what can be said about their lengths?

Back

The lengths of the two tangent segments from the external point to the circle are equal.

Front

What is the formula for the area of a sector of a circle?

Back

The area of a sector is given by the formula: \( A = \frac{\theta}{360} \times \pi r^2 \), where \( \theta \) is the angle in degrees and \( r \) is the radius.

Front

How do you calculate the arc length of a circle?

Back

The arc length can be calculated using the formula: \( L = \frac{\theta}{360} \times 2\pi r \), where \( \theta \) is the angle in degrees and \( r \) is the radius.