Answer: GI = 7.2
Step-by-step explanation:
Recall; from the same external point, the tangent segment segments to a circle are equal. From the information given,
GH and GI are tangents from an external point G. This means that
GH = GI
Also, the angle formed by the tangent, GH and the radius OH is 90 degrees. This means that triangle GHO is a right angle triangle. We would find GH by applying the Pythagorean theorem which is expressed as
hypotenuse^2 = one leg^2 + other leg^2
Considering triangle GHO,
one leg = GH
other leg = OH = 6.5
hypotenuse = GO = 9.7
Thus,
9.7^2 = GH^2 + 6.5^2
GH^2 = 9.7^2 - 6.5^2 = 51.84
GH = √51.84
GH = 7.2
Since GH = GI,
GI = 7.2H