Warm Up Solve the quadratic equations 1 x

Warm Up Solve the quadratic equations. 1) x² + 4 x = 25 2) x² + 18 x = 144

Answers to Warm Up •

Answers to Warm Up 2. x² + 18 x = 144 (need to get the equation = 0 first) x² + 18 x – 144 = 0 (can factor or usee quadratic formula) (x + 24)(x – 6) = 0 (set each factor = 0 and solve) (x + 24) = 0 (x – 6) = 0 x = -24 and 6

Segment Length Properties Advanced Geometry

Examine the Circle

THEOREM If two chords intersect in the interior of a circle, then the product of the lengths of the segments of one chord is equal to the product of the lengths of the segments of the other chord. AE · ED = BE · EC

THOEREM

Find x

Find x

Find x

Segments of Tangents and Secants

Investigate 2 Secants

THEOREM If two secant segments share the same endpoint outside a circle, then the product of the length of one secant segment and the length of its external segment equals the product of the length of the other secant segment and the length of its external segment. EC · EA = ED · EB

Example

Find x

Example

Example

Investigate a Tangent & a Secant

THEOREM If a secant segment and a tangent segment share an endpoint outside a circle, then the product of the length of the secant segment and the length of its external segment equals the square of the length of the tangent segment. AB · AC = AD²

Find x.

Example

Example

Example