Question

given the circle below with secants ghi and kji, find the length of gh. round to the nearest tenth if necessary.

Explanation:

Step1: Use the secant - secant formula

If two secants are drawn from an external point \(I\) to a circle, then \(IK\times IJ=IG\times IH\). Let \(GH = x\), then \(IG=11 + x\), \(IK = 8+12=20\), and \(IJ = 12\).
So, \(20\times12=(11 + x)\times11\).

Step2: Expand and solve the equation

First, expand the right - hand side: \(240 = 121+11x\).
Then, subtract 121 from both sides: \(11x=240 - 121\).
\(11x = 119\).
Divide both sides by 11: \(x=\frac{119}{11}\approx10.8\).

Answer:

\(10.8\)