Line segments in Circles

Front

What is a tangent to a circle?

Back

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

Front

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

Back

A tangent to a circle is perpendicular to the radius drawn to the point of tangency.

Front

If QS is a tangent to circle P and the length of QS is 12, what can we conclude about the radius at the point of tangency?

Back

The radius at the point of tangency is perpendicular to QS.

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 \( d \) is the distance from the point to the center of the circle and \( r \) is the radius.

Front

If two tangent segments are drawn from a single external point to a circle, what can be said about their lengths?

Back

The lengths of the two tangent segments are equal.

Front

What is the value of x if a tangent segment measures 10 units and the radius to the point of tangency measures 6 units?

Back

Using the Pythagorean theorem, \( x = \sqrt{10^2 - 6^2} = \sqrt{64} = 8 \).

Front

If a tangent segment measures 2 units and the radius to the point of tangency measures 2 units, what is the distance from the external point to the center of the circle?

Back

Using the Pythagorean theorem, the distance is \( d = \sqrt{2^2 + 2^2} = \sqrt{8} = 2\sqrt{2} \).

Front

What is the definition of a secant line?

Back

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

Front

How do you find the angle formed between a tangent and a chord through the point of tangency?

Back

The angle formed between a tangent and a chord through the point of tangency is equal to the measure of the opposite angle formed by the chord.

Front

What is the relationship between the angles formed by two intersecting chords in a circle?

Back

The measure of the angle formed by two intersecting chords is equal to half the sum of the measures of the arcs intercepted by the angle and its vertical angle.