8 6 Segments in Circles Interior Segments l

8 -6 Segments in Circles

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

Interior Segments Theorem l 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 l 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 D a c C d E a • b = c • d b B

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

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

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: l The square of the length of the tangent equals the product of the length of the secant and its exterior segment. s • e = t 2 t e s

Secant and Tangent Theorem: s • e = t 2

EXAMPLE: x FIND x

Review: Tangent Theorem l. If two segments from the same exterior point are tangent to a circle, then they are congruent. tan gen t g n ta t n e