(Geometry: point in a circle?) Write a program that prompts...

(Geometry: point in a circle?) Write a program that prompts the user to enter a point $(x, y)$ and checks whether the point is within the circle centered at (0,0) with radius $10 .$ For example, (4,5) is inside the circle and (9,9) is outside the circle, as shown in Figure 3.9 a. (Hint: A point is in the circle if its distance to (0,0) is less than or equal to $10 .$ The formula for computing the distance is $\sqrt{\left(x_{2}-x_{1}\right)^{2}+\left(y_{2}-y_{1}\right)^{2}} .$ Test your program to cover all cases.) Two sample runs are shown below. Enter a point with two coordinates: 45 Point (4.0,5.0) is in the circle Enter a point with two coordinates: 99 Point (9.0,9.0) is not in the circle

(Geometry: point in a circle?) Write a program that prompts the user to enter a point $(x, y)$ and checks whether the point is within the circle centered at (0,0) with radius $10 .$ For example, (4,5) is inside the circle and (9,9) is outside the circle, as shown in Figure 3.9 a.
(Hint: A point is in the circle if its distance to (0,0) is less than or equal to $10 .$ The formula for computing the distance is $\sqrt{\left(x_{2}-x_{1}\right)^{2}+\left(y_{2}-y_{1}\right)^{2}} .$ Test your program to cover all cases.) Two sample runs are shown below.
Enter a point with two coordinates: 45 Point (4.0,5.0) is in the circle
Enter a point with two coordinates: 99 Point (9.0,9.0) is not in the circle

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Key Concepts

Circle Equation

A circle in the coordinate plane can be defined by an equation that represents all points equidistant from a fixed center point. For a circle centered at (0,0) with radius r, the equation is x² + y² = r². This equation, or its inequality version for points inside or on the circle, is fundamental for problems that involve determining the relationship between a point and the circle.

Conditional Logic in Programming

Conditional logic in programming involves using if-else statements to make decisions based on whether a certain condition is true or false. In the context of checking if a point is within a circle, the program uses a conditional statement to compare the computed distance from the point to the center with the circle's radius, allowing the program to output the appropriate result.

Distance Formula

The distance formula calculates the straight-line distance between two points in the coordinate plane. It is derived from the Pythagorean theorem and is expressed as ?((x2 - x1)² + (y2 - y1)²). In problems involving circles, it is used to determine how far a point is from the center of the circle, which is essential for checking whether the point lies inside, on, or outside the circle.

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