T-X vs T-850

Time limit: 2000 ms. Memory limit: 1024 MB.

I'm back!

T-850

The T-850 terminator has returned to face the Skynet computer network again. This time Skynet sends its newest invention against it, the terminator T-X, built to destroy T-850 and start Judgment Day.

The fight takes place in open terrain with only one building. The building is a circle of radius $r$ centered at $(x_c, y_c)$. T-850 is at $(x_1, y_1)$ and T-X is at $(x_2, y_2)$. T-850 wants to fire at T-X, but it can do so only if it can see T-X.

T-850 sees T-X only if the segment connecting them does not intersect the wall of the building. Help the programmers from the future who write T-850's software handle even this case and determine whether T-850 can fire at T-X at this moment.

The first line contains the number of queries $t$ ($1 \le t \le 5$). Each query consists of three lines.

The first line gives the building's coordinates and radius $x_c$, $y_c$, $r$. The second line gives the coordinates of T-850, $x_1$, $y_1$. The third line gives the coordinates of T-X, $x_2$, $y_2$.

All numbers in the input are integers with absolute value at most 100. It is guaranteed that the distance from the line through $(x_1, y_1)$ and $(x_2, y_2)$ to $(x_c, y_c)$ differs from $r$ by more than $10^{-5}$. It is also guaranteed that neither T-X nor T-850 lies on the boundary of the building.

For each query, print YES if T-850 can fire at T-X, and NO otherwise.