简单几何题 - Problem

#12060. 简单几何题

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AI Translation — This statement was translated using AI and may contain inaccuracies. Please refer to the original statement if in doubt.

设 $ABCD$ 是一个四面体，已知 $DA = a, DB = b, DC = c, \angle BDC = \alpha, \angle ADC = \beta, \angle ADB = \gamma$。

你需要计算四面体 $ABCD$ 的内切球半径。

输入格式

第一行包含一个整数 $T$ ($1 \le T \le 100000$)，表示测试用例的数量。

每个测试用例包含六个整数 $a, b, c, \alpha, \beta, \gamma$。

($1 \le a, b, c \le 100, 0 < \alpha, \beta, \gamma < 360$)

输出格式

输出内切球的半径。请保留小数点后 6 位。

样例

样例输入 1

1
10 10 10 90 90 90

样例输出 1

2.113249

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