Question

what is gi? gi =

Explanation:

Step1: Assume H is the circum - center.

Since H is the circum - center of \(\triangle GHI\), \(GH = HI\). And \(FH\) is a perpendicular bisector of \(GI\). Let \(GH = HI\), then \(s + 21=4s\).

Step2: Solve the equation for s.

Subtract \(s\) from both sides of the equation \(s + 21=4s\): \(21=4s - s\), so \(3s=21\), and \(s = 7\).

Step3: Find the length of \(GI\).

Since \(FH\) is a perpendicular bisector of \(GI\), \(GI = 2\times FI\). And \(FI=4s\), substituting \(s = 7\), we get \(FI = 4\times7=28\). So \(GI=2\times28 = 56\).

Answer:

56