12/6/24 Intersecting chords, secants and tangents

Front

What is the definition of a tangent in relation to a circle?

Back

A tangent is a line that touches a circle at exactly one point, known as the point of tangency.

Front

State the Tangent-Secant Theorem.

Back

The Tangent-Secant Theorem states that if a tangent and a secant intersect at a point outside a circle, then the square of the length of the tangent segment is equal to the product of the lengths of the secant segment and its external part.

Front

What is the formula for finding the angle formed by two intersecting chords?

Back

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.

Front

If two chords intersect inside a circle, how do you find the lengths of the segments?

Back

The products of the lengths of the segments of each chord are equal. If chord AB intersects chord CD at point E, then AE * EB = CE * ED.

Front

What is the relationship between the angles formed by two secants that intersect outside a circle?

Back

The angle formed by two secants that intersect outside a circle is equal to half the difference of the measures of the intercepted arcs.

Front

How do you calculate the length of a tangent segment from a point outside the circle?

Back

The length of the tangent segment can be calculated using the formula: length = √(distance from the point to the center of the circle² - radius²).

Front

What is the definition of a secant line?

Back

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

Front

Explain the concept of intercepted arcs.

Back

Intercepted arcs are the arcs that lie in the interior of an angle formed by two lines (chords, secants, or tangents) that intersect the circle.

Front

What is the formula for the angle formed by a tangent and a chord through the point of contact?

Back

The angle formed by a tangent and a chord through the point of contact is equal to the measure of the intercepted arc.

Front

If a tangent and a secant intersect at a point outside the circle, what is the relationship between the tangent and the secant?

Back

The square of the length of the tangent segment is equal to the product of the lengths of the secant segment and its external part.