Choose numbers with a particular product

Learning Objectives Identify the correct theorem for intersecting chords, secants, and tangents. Apply the Intersecting Chords Theorem to find unknown segment lengths. Use the Secant-Secant and Tangent-Secant theorems to solve for unknown lengths. Calculate the constant product, known as the 'Power of a Point', for a given geometric configuration. Choose different pairs of integer lengths for segments that satisfy a particular product. Set up and solve algebraic equations derived from circle theorems. What if you could find a hidden multiplication rule inside every circle? 🧐 Let's explore the secret constant product that connects intersecting lines! In this tutorial, we will uncover the powerful relationship between the segments formed by intersecting chords...

TermDefinitionExample ChordA line segment whose two endpoints lie on the circle.If you draw a line from one side of a pizza crust to the other without passing through the center, that's a chord. SecantA line that passes through a circle, intersecting it at two distinct points.Imagine a laser beam passing through a planet; the path of the beam is a secant line. TangentA line that touches a circle at exactly one point, called the point of tangency.A ruler resting on the side of a ball is tangent to the ball. Power of a PointA constant value calculated by multiplying the lengths of segments formed by a line passing through a given point and a circle. This product is the same for any line passing through that point.If two chords intersect, and the segments of one are 2 and 6, the Power o...

Intersecting Chords Theorem a \cdot b = c \cdot d When two chords intersect inside a circle, the product of the segments of one chord (a and b) is equal to the product of the segments of the other chord (c and d). Secant-Secant Theorem a \cdot (a+b) = c \cdot (c+d) When two secants are drawn from an external point, the product of the length of the whole first secant (a+b) and its external part (a) equals the product of the length of the whole second secant (c+d) and its external part (c). Tangent-Secant Theorem t^2 = a \cdot (a+b) When a tangent and a secant are drawn from an external point, the square of the tangent's length (t) equals the product of the length of the whole secant (a+b) and its external part (a).