Question

help plsSolve for [x]. Assume that lines which appear Tangent are Tangent. Find EGa) 21b) 17c) 10d) 12

Answer 1

In the given figure two chords intersect at a point inside a circle.

From the theorem of the intersecting chords,

$\begin{gathered} FS\times SD=ES\times SG \\ 9\times10=(x-3)\times(x+6) \\ 90=x^2+6x-3x-18 \\ x^2+3x-18-90=0 \\ x^2+3x-108=0 \\ x^2+12x-9x-108=0 \\ x(x+12)-9(x+12)=0 \\ (x+12)(x-9)=0 \\ x=-12\text{ and 9} \end{gathered}$

Ignoring the negative value of x, the value of EG can be determined as,

$\begin{gathered} EG=ES+SG \\ =(x-3)+(x+6) \\ =2x+3 \\ =2(9)+3 \\ =18+3 \\ =21 \end{gathered}$

Thus, option (A) is the correct option.