This is a 4th example for the first OpenGL lesson

PolygonInCircle.cpp

//
//  main.cpp
//  OpenGL-examples
//
//  Created by Alexey Potapov on 27.09.14.
//  Copyright (c) 2014 none. All rights reserved.
//

#include <stdlib.h>
#include <stdio.h>
#include <iostream>
#include <math.h>

#if defined (__APPLE__)
    #include <GLUT/glut.h>
#else
    #include <GL/glut.h>
#endif

float Pi = 3.1415926;
int verticesCount;

void keyboardListener (unsigned char key, int x, int y)
{
    switch ((char)key)
    {
        case 'q':
        case 27:
            exit(0);
            break;
        default:
            break;
    }
}

void numberOfVertices()
{
    printf("Please input integer variable!\nVertices count: ");
    std::cin >> verticesCount;
    while (!std::cin)
    {
        std::cin.clear();
        std::cin.ignore(256,'\n');
        printf("Once more time!\nVertices count: ");
        std::cin >> verticesCount;
    }
}

//inspired by http://slabode.exofire.net/circle_draw.shtml
void drawFigure(float cx, float cy, float r, int num_segments)
{
    float theta = 2 * Pi / float(num_segments);
    float c = cosf(theta);//precalculate the sine and cosine
    float s = sinf(theta);
    float t;
    
    float x = r;//we start at angle = 0
    float y = 0;
    
    glBegin(GL_LINE_LOOP);
    for(int ii = 0; ii < num_segments; ii++)
    {
        glVertex2f(x + cx, y + cy);//output vertex
        //apply the rotation matrix
        t = x;
        x = c * x - s * y;
        y = s * t + c * y;
    } 
    glEnd();
}

void displayProcess (void)
{
    glClear(GL_COLOR_BUFFER_BIT);
    glLoadIdentity();
    //draw cirle
    glColor3f(1, 1, 1);
    drawFigure(0, 0, 1, 50);
    //draw red polygon
    glColor3f(1, 0, 0);
    drawFigure(0, 0, 1, verticesCount);
    
    glFlush();
    glutSwapBuffers();
}

void openGLfunction (int argc, char *argv[])
{
    glutInit(&argc, argv);
    glutInitDisplayMode(GLUT_DOUBLE | GLUT_RGB);
    glutInitWindowSize(400, 400);
    glutCreateWindow("Polygon inside the circle");
    glutDisplayFunc(displayProcess);
    glutKeyboardFunc(keyboardListener);
    
    glutMainLoop();
}

int main(int argc, char *argv[])
{
    numberOfVertices();
    openGLfunction(argc, argv);
    return 0;
}