Fifa and Fafa

题意翻译

给定一个半径为$R$的圆，圆心坐标$(x_1,y_1)$。请找到圆内一点$C(x_{ap},y_{ap})$和一个半径$r$，使得以$C$为圆心、以$r$为半径的圆不超出大圆，并且点$(x_2,y_2)$（不一定在大圆内）不在此圆内（可以在圆周上）。求大圆的未覆盖面积最小时$x_{ap}$、$y_{ap}$和$r$的值。 $R$、$x_1$、$y_1$、$x_2$、$y_2$均为整数，$x_{ap}$、$y_{ap}$和$r$均为实数。

题目描述

Fifa and Fafa are sharing a flat. Fifa loves video games and wants to download a new soccer game. Unfortunately, Fafa heavily uses the internet which consumes the quota. Fifa can access the internet through his Wi-Fi access point. This access point can be accessed within a range of $ r $ meters (this range can be chosen by Fifa) from its position. Fifa must put the access point inside the flat which has a circular shape of radius $ R $ . Fifa wants to minimize the area that is not covered by the access point inside the flat without letting Fafa or anyone outside the flat to get access to the internet. The world is represented as an infinite 2D plane. The flat is centered at $ (x_{1},y_{1}) $ and has radius $ R $ and Fafa's laptop is located at $ (x_{2},y_{2}) $ , not necessarily inside the flat. Find the position and the radius chosen by Fifa for his access point which minimizes the uncovered area.

输入输出格式

输入格式

The single line of the input contains 5 space-separated integers $ R,x_{1},y_{1},x_{2},y_{2} $ ( $ 1<=R<=10^{5} $ , $ |x_{1}|,|y_{1}|,|x_{2}|,|y_{2}|<=10^{5} $ ).

输出格式

Print three space-separated numbers $ x_{ap},y_{ap},r $ where $ (x_{ap},y_{ap}) $ is the position which Fifa chose for the access point and $ r $ is the radius of its range. Your answer will be considered correct if the radius does not differ from optimal more than $ 10^{-6} $ absolutely or relatively, and also the radius you printed can be changed by no more than $ 10^{-6} $ (absolutely or relatively) in such a way that all points outside the flat and Fafa's laptop position are outside circle of the access point range.

输入输出样例

输入样例 #1

5 3 3 1 1

输出样例 #1

3.7677669529663684 3.7677669529663684 3.914213562373095

输入样例 #2

10 5 5 5 15

输出样例 #2

5.0 5.0 10.0