NOTES 10 8 The Power Theorems Theorem 95

NOTES 10. 8 The Power Theorems

Theorem 95: § If two chords of a circle intersect inside the circle, then the product of the measures of the segments of one chord is equal to the product of the measures of the segments of the other chord. (Chord-Chord Power Theorem) part • part = part • part

Solve for x: § 6 • 2 = 3 x § 12 = 3 x § x=4

Theorem 96: § If a tangent segment and a secant segment are drawn from an external point to a circle, then the square of the measure of the tangent segment is equal to the product of the measures of the entire secant segment and its external part. (Tangent-Secant Power Theorem) tan 2 = part • total

Solve for y: § y 2 = 2 • 18 § y = ± 6 (reject -6) § y=6

Theorem 97: § If two secant segments are drawn from an external point to a circle, then the product of the measures of one secant and its external part is equal to the product of the measures at the other secant segment and its external part. (Secant-secant Power Theorem) part • total = part • total

Solve for z: 4 • (8 + 4) = 3 z 4 • 12 = 3 z 16 = z

Tangent segment PT measures 8 cm. The radius of the circle is 6 cm. Find the distance from P to the circle. Draw a picture of tangent PT. § Draw a secant segment from P through the center of the circle. § Use Tangent-Secant Power Theorem. § (PQ)(PS)=(PT)2 § x(x + 12) = 82 § x 2 + 12 x – 64 = 0 § (x – 4)(x + 16) = 0 § x = 4 or -16 § § PQ = 4 cm