The segment GH and GI are tangent

  OG = 8.7

Step-by-step explanation:

The angle a tangent makes with a radius at the point of tangency is a right angle. That means ΔOGH is a right triangle.

The tangents to a circle from an external point are congruent, so GH = GI = 6.3. Now we know the sides of the right triangle are of lengths 6 and 6.3. The hypotenuse, OG is found using the Pythagorean theorem.

  OG² = OH² +GH²

  OG² = 6² +6.3² = 75.69

  OG = √75.69 = 8.7

The length of OG is 8.7 units.

Additional comment

You might recognize this triangle as a 0.3 multiple of the Pythagorean triple (20, 21, 29).

step-by-step explanation: