Question

what is the value of x? 2 3 6 7

Explanation:

Step1: Apply the secant - secant rule

If two secant segments are drawn to a circle from an external point, then \((EA)(EB)=(ED)(EC)\). Here, \(EA = 11+(x + 1)=x + 12\), \(EB=x + 1\), \(ED=1+(x + 4)=x+5\), \(EC=x + 4\).

Step2: Substitute into the formula

\((x + 12)(x + 1)=(x + 5)(x + 4)\)
Expand both sides:

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Step3: Simplify the equation

Subtract \(x^{2}\) from both sides: \(13x + 12=9x+20\).
Subtract \(9x\) from both sides: \(13x-9x+12=9x - 9x+20\), so \(4x+12 = 20\).
Subtract 12 from both sides: \(4x+12-12=20 - 12\), then \(4x=8\).
Divide both sides by 4: \(x=\frac{8}{4}=2\).

Answer:

2