Which of the following coral reefs is horse shoe shaped reef that encircles a lagoon but not an island?
1)Atoll reef
2 Fringing reefs
3) Barrier reefs
4) Hawaiian island

Options

A. Atoll reef
B. Fringing reefs
C. Barrier reefs
D. Hawaiian island

Explanation

To answer the question "Which of the following coral reefs is a horseshoe-shaped reef that encircles a lagoon but not an island?", we will analyze the options provided:

1. **Atoll Reef**: Atolls are coral reefs that are typically circular or horseshoe-shaped and encircle a lagoon. They do not form around an island but rather are found in open water. This matches the description given in the question.

2. **Fringing Reefs**: These reefs are directly attached to the shore of a landmass and do not encircle a lagoon. They grow in shallow waters and are not horseshoe-shaped.

3. **Barrier Reefs**: Barrier reefs are similar to fringing reefs but are separated from the shore by a lagoon. They can be extensive but do not have the horseshoe shape characteristic of atolls.

4. **Hawaiian Island**: This is not a type of coral reef but rather a landmass. Therefore, it does not fit the description of a reef that encircles a lagoon.

Based on this analysis, the correct answer is:

**Atoll Reef**.

### Step-by-Step Solution:
1. **Understand the Question**: Identify what is being asked - a coral reef that is horseshoe-shaped and encircles a lagoon but not an island.
2. **Define Coral Reefs**: Recognize that coral reefs are formed by colonies of polyps and can take various shapes.
3. **Analyze the Options**:
- Atoll Reef: Matches the description.
- Fringing Reef: Does not match; attached to the shore.
- Barrier Reef: Does not match; not horseshoe-shaped.
- Hawaiian Island: Not a reef type.
4. **Select the Correct Answer**: Conclude that the only option that fits the description is the Atoll Reef.