Question

Составьте программу, определяющую, лежит ли точка с указанными координатами X, Y на окружности радиуса R с центром в начале координат. Program Frankenstein;varx,y,r:integer;Begin Write('Введите координату X: ');Readln(x); Write('Введите координату Y: ');Readln(y); Write('Введите длину радиуса R: '); Readln(r);If (sqr(x)+sqr(y))=rthen writeln('Точка лежит на окружности!') Else writeln('Точка не лежит на окружности!'); End. Почему программа всегда показывает что точка не лежит на окружности, хотя на самом деле она лежит! Где я ошибся?

Answer 1

Var
x,y,r:integer;
Begin
Write('Введите координату X: ');
Readln(x);
Write('Введите координату Y: ');
Readln(y);
Write('Введите длину радиуса R: ');
Readln(r);
If (sqr(x)+sqr(y))=sqr(r)  then 
writeln('Точка лежит на окружности!')
Else writeln('Точка не лежит на окружности!');
End.

Answer 2

Understanding the Code

The provided code is written in Pascal and aims to determine whether a point with the given coordinates (X, Y) lies on a circle with a specified radius (R) and a center at the origin (0, 0). The program prompts the user to input the values for X, Y, and R and then performs a calculation to check if the point lies on the circle.

Analyzing the Issue

The issue seems to be that the program always outputs that the point does not lie on the circle, even when it actually does. We will analyze the code to identify the potential error.

Code Analysis

Let's break down the code and analyze it step by step:

Program Frankenstein;
var
  x, y, r: integer;
Begin
  Write('Введите координату X: ');
  Readln(x);
  Write('Введите координату Y: ');
  Readln(y);
  Write('Введите длину радиуса R: ');
  Readln(r);
  
  If (sqr(x) + sqr(y)) = r then
    writeln('Точка лежит на окружности!')
  Else
    writeln('Точка не лежит на окружности!');
End.

The issue lies in the comparison `(sqr(x) + sqr(y)) = r`. This comparison checks if the sum of the squares of the coordinates (X^2 + Y^2) is equal to the radius (R). However, this condition will rarely be true, as the sum of the squares of the coordinates is not equal to the radius of a circle.

Correcting the Code

To determine if a point lies on a circle, we need to compare the distance between the point and the center of the circle with the radius of the circle. The correct condition should be `(sqr(x) + sqr(y)) = sqr(r)`.

Here's the corrected code:

Program Frankenstein;
var
  x, y, r: integer;
Begin
  Write('Введите координату X: ');
  Readln(x);
  Write('Введите координату Y: ');
  Readln(y);
  Write('Введите длину радиуса R: ');
  Readln(r);
  
  If (sqr(x) + sqr(y)) = sqr(r) then
    writeln('Точка лежит на окружности!')
  Else
    writeln('Точка не лежит на окружности!');
End.

Explanation

In the corrected code, we compare `(sqr(x) + sqr(y))` with `sqr(r)` to check if the point lies on the circle. The `sqr()` function is used to calculate the square of a number. By comparing the sum of the squares of the coordinates with the square of the radius, we can accurately determine if the point lies on the circle.

Now, when you run the program and input the coordinates and radius, it will correctly determine whether the point lies on the circle or not.

I hope this explanation helps! Let me know if you have any further questions.