Question

Examine the diagram, where BD¯¯¯¯¯¯¯¯

Answer 1

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:

$AB \times EB= DB^{2}$

AB = $(x-7)+4 = x -3$

EB = 4

• Substitute:

$(x - 3)(4) = 8^{2} \\\\4x - 12 = 64$

• Add 12 to both sides

$4x = 64 +12\\\\4x = 76$

• Divide both sides by 4

x = 19

Therefore the value of x is 19.

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