8-6 Segments in Circles

Interior Segments Interior segments are formed by two intersecting chords. A B C D E

Interior Segments Theorem If two chords intersect within a circle, then the product of the lengths of the parts of one chord is equal to the product of the lengths of the parts of the second chord.

Interior Segments Theorem If two chords intersect within a circle, then the product of the lengths of the parts of one chord is equal to the product of the lengths of the parts of the second chord. A B C D E a d a•b = c•d b c

Exterior Segments Exterior segments are formed by two secants, or a secant and a tangent, or two tangents.

Secant Segments Theorem If two secant segments are drawn to a circle from an external point, then the products of the lengths of the secant and their exterior parts are equal. s•e = r•c secant•exterior = secant•exterior or whole•outside = whole•outside wo = wo s e c r

Secant Segments Theorem s•e = r•c secant•exterior = secant•exterior or whole•outside = whole•outside wo = wo

EXAMPLE: x FIND x

Secant and Tangent Theorem: The square of the length of the tangent equals the product of the length of the secant and its exterior segment. s•e = t2 t e s

Secant and Tangent Theorem: s•e = t2

EXAMPLE: x FIND x

Review: Tangent Tangent Theorem If two segments from the same exterior point are tangent to a circle, then they are congruent. tangent tangent