Respuesta :

frika

Answer:

KP=12

Step-by-step explanation:

Use property for circle and tangent segment:

tangent segment² = external secant segment · secant segment.

In your case,

tangent segment KE = 18;

external secant segment KP;

secant segment KL = KP + 15.

Thus,

18²=KP(KP+15),

KP²+15KP-324=0,

D=15^2-4·(-324)=225+1296=1521,

KP=(-15±39)/2=-27, 12.

The segment cannot be of negative length, then KP=12.

isyllus

Answer:

The length of KP = 12 unit.

Step-by-step explanation:

Given: Circle with center O. KE is tangent at E and PL is diameter.

KE=18, PL=15 find KP

Let length of KP be x

Tangent- Secant Theorem: The square of length of tangent is equal to product of length of sub part of secant.

[tex]KE^2=KP\cdot KL[/tex]

KE = 18

KP = x

KL= x+15

[tex]18^2=x(x+15)[/tex]

[tex]x^2+15x-324=0[/tex]

[tex](x+27)(x-12)=0[/tex]

Set each factor to 0 and solve for x

[tex]x+27=0\Rightarrow x=-27[/tex]

[tex]x-12=0\Rightarrow x=12[/tex]

We will ignore negative value of x because length can't be negative.

Hence, The length of KP = 12 unit.

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