Final answer:
The length of segment OC, which is the radius of the circle, is found using the Pythagorean Theorem in the right triangle OCD, with the given lengths OD = 9.6 units and CE = 11 units. The computation concludes with OC being approximately 14.6 units.
Step-by-step explanation:
The student is dealing with a geometry problem involving a circle and tangent segments. To find the length of segment OC, which is the radius of the circle when a tangent from point C touches the circle at D, we can use the Pythagorean Theorem in right triangle OCD, where OD is the radius and CD (equal to CE) is the tangent from C to the circle.
Since tangent segments from a common external point are congruent, we know that CD = CE = 11 units. We have OD = 9.6 units, and we are trying to find OC. By applying the Pythagorean Theorem to right triangle OCD:
- OD2 + CD2 = OC2
- 9.62 + 112 = OC2
- 92.16 + 121 = OC2
- 213.16 = OC2
- √213.16 = OC
- OC ≈ 14.6 units (to two decimal places)
Therefore, the length of segment OC is approximately 14.6 units.