contestada

In Circle O, secants ADB and AEC are drawn from external point A such that points D, B, E, and C are on Circle O. If AD=8, AE=6, and EC is 12 more than BD, find the length of AC.

Respuesta :

frika

Answer:

40 units

Step-by-step explanation:

If two secants are drawn to a circle from one exterior point, then the product of the external segment and the total length of each secant are equal.

Thus,

[tex]AC\cdot AE=AB\cdot AD.[/tex]

Since AD=8 units, AE=6 units , EC=12+BD units, then

[tex]AC=AE+EC=6+12+BD=18+BD\ units,[/tex]

[tex]AB=AD+DB=8+BD\ units.[/tex]

Therefore,

[tex](18+BD)\cdot 6=(8+BD)\cdot 8,\\ \\108+6BD=64+8BD,\\ \\2BD=44,\\ \\BD=22\ units[/tex]

and

[tex]AC=18+22=40\ units.[/tex]

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