Incenter of the triangle formed by the lines whose are $3x+4y=0;5x-12y=0$ and $y-15=0$ is the point $P$ whose coordinates are $(1,8)$

Question

This is a reasoning type question.
Statement$(1):$Incenter of the triangle formed by the lines whose are $3x+4y=0;5x-12y=0$ and $y-15=0$ is the point $P$ whose coordinates are $(1,8)$.

Statement$(2):$Point $P$ is equidistant from the 3 lines forming the triangle.

$(A)$Statement-$1$ is true,statement-$2$ is true and statement-$2$ is correct explanation for statement-$1$.
$(B)$Statement-$1$ is true,statement-$2$ is true and statement-$2$ is NOT correct explanation for statement-$1$.
$(C)$Statement-$1$ is true,statement-$2$ is false
$(D)$Statement-$1$ is false,statement-$2$ is true

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I solved this question and i chose $(A)$ is the correct answer but the book says $(B)$ is the correct answer.I could not understand why $(A)$ is not the correct answer and $(B)$ is the correct answer.As incenter is equidistant from the three sides of the triangle.Is there some point,different from incenter,also which is equidistant from the three sides of the triangle?

Please help me.

Answer 1

Yes the point is known as circumcenter which is equidistant from all vertices of a triangle and incentre may or may not be equidistant.