f P is a point in the interior of a circle of a circle with centre o and radius r, thena. OP=r b. OP>r c. OP≥r d. OP<r

To solve the problem, let’s analyze the geometric relationship between the point P, the center O of the circle, and the radius r of the circle.

1. ### Break Down the Problem

1. We have a circle with center O and radius r.
2. Point P is located in the interior of this circle.
3. We need to determine the relationship between the distance OP and the radius r.

2. ### Relevant Concepts

• The definition of a circle: All points on the circle are at a distance r from the center O.
• A point is inside the circle if its distance from the center is less than the radius.

3. ### Analysis and Detail

• Since point P is in the interior of the circle, by definition, the distance from the center O to point P (denoted as OP) must be less than the radius of the circle (r).
• Therefore, we can represent this relationship mathematically as: $OP < r$

4. ### Verify and Summarize

• Since OP, the distance from the center O to point P, is less than the circle's radius (r), we confirm that the only viable answer based on these considerations is that OP must be less than r.

Final Answer

The correct choice is d. OP < r.