Segment Lengths in Circles Interior Segments Interior segments

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

Example B In the circle, AX = 3, XC = 8, and DX =

Another Example Solve for x. 6 12(x + 1) = (6)(32) 12 x +

Exterior Segments • Exterior segments are formed by two secants, or a secant and

Outside x Whole = Outside x Whole e a b c d f a

Example In circle P, AB = 60, BX = 13, and DX = 15.

Another Example 18 Find y 5 6 y Outside x Whole = Outside x

Secant and Tangent Outside x Whole = (Tangent)2 a b c d a 2

Example CX is tangent to the circle. If BX = 24, and CX =

Final Example!! Given: AB is tangent to circle P at B, AH = 9,

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Segment Lengths in Circles

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

A d a E c D b B C a • b = c • d

Example B In the circle, AX = 3, XC = 8, and DX = 5. Find XB. (3)(8) = 5 y 24/5 = 4. 8 = y A y 3 5 D X 8 C

Another Example Solve for x. 6 12(x + 1) = (6)(32) 12 x + 12 = 192 12 x = 180 x = 15 12 x+1 32

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

Outside x Whole = Outside x Whole e a b c d f a • e = c • f

Example In circle P, AB = 60, BX = 13, and DX = 15. Find CD. A 60 B 13 X P D 15 y C Outside x Whole = Outside x Whole (13)(73) = 15(y + 15) 949 = 15 y + 225 724 = 15 y 724/15 = y

Another Example 18 Find y 5 6 y Outside x Whole = Outside x Whole (5)(23) = 6(y + 6) 115 = 6 y + 36 79 = 6 y 79/6 = y

Secant and Tangent Outside x Whole = (Tangent)2 a b c d a 2 = b • d

Example CX is tangent to the circle. If BX = 24, and CX = 30, find AX. y A B P 24 X 30 C Outside x Whole = (Tangent)2 24 y = 302 24 y = 900/24 = 75/2 = 37. 5

Final Example!! Given: AB is tangent to circle P at B, AH = 9, HC = 16, and AG = 10 Find AB and AD. To find AB: 10 9 To find AD: (9)(25) = AB 2 225 = AB 2 15 = AB (9)(25) = 10 AD 225 = 10 AD 22. 5 = AD 16