Introduction:
In a power transistor, the collector current (IC) is controlled by the base current (IB) through the relationship known as the transistor's current gain, beta (β). The current gain, β, is defined as the ratio of the collector current to the base current (β = IC/IB). When the base current is increased while keeping the collector-emitter voltage (VCE) constant, the collector current also increases.

Explanation:
When the base current is increased while keeping the collector-emitter voltage constant in a power transistor, the following changes occur:

1. Base-Collector Junction:
- The base-collector junction is forward-biased, allowing current to flow from the base to the collector.
- As the base current increases, more charge carriers are injected into the base region, leading to an increase in the number of charge carriers available for collection in the collector region.

2. Current Gain (β):
- The current gain, β, represents the multiplication factor between the base current and the collector current.
- In an ideal power transistor, β is constant over a specified range of operating conditions.
- When the base current is increased, the current gain amplifies the change, resulting in a larger increase in the collector current.

3. Collector Current (IC):
- The collector current is directly proportional to the base current according to the current gain, β.
- Therefore, when the base current is increased, the collector current also increases.

Conclusion:
In summary, when the base current in a power transistor is increased while keeping the collector-emitter voltage constant, the collector current increases due to the forward-biased base-collector junction and the amplification effect of the current gain, β. Therefore, the correct answer is option 'A' - IC increases.