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Examine the diagram, where BD¯¯¯¯¯¯¯¯
B
D
¯
is tangent to circle M
at point D,
and BA¯¯¯¯¯¯¯¯
is secant to the same circle at points E and A.

Examine the diagram where BD B D is tangent to circle M at point D and BA is secant to the same circle at points E and A class=

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akposevictor

The value of x based on the tangent-secant theorem is: 19.

Recall:

  • The secant-tangent theorem states that when a tangent and a secant meet outside a circle, the product of the secant length and it's segment outside the circle is equal to the square of the tangent segment length.

  • Applying the tangent-secant theorem or rule, we will have this equation:

[tex]AB \times EB= DB^{2}[/tex]

AB = [tex](x-7)+4 = x -3[/tex]

EB = 4

  • Substitute:

[tex](x - 3)(4) = 8^{2} \\\\4x - 12 = 64\\\\[/tex]

  • Add 12 to both sides

[tex]4x = 64 +12\\\\4x = 76[/tex]

  • Divide both sides by 4

x = 19

Therefore the value of x is 19.

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