60.9k views
14 votes
The segment GH and GI are tangent

The segment GH and GI are tangent-example-1

1 Answer

6 votes

Answer:

OG = 8.7

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).

User Finder
by
8.9k points
Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories