The line $3x + 4y - 24 = 0$ meets the $x$-axis at $A$ and $y$-axis at $B$. The incentre of $\Delta OAB$, where $O$ is the origin, is:
Step-by-Step Solution
Key Concept: Find $A = (8, 0)$ and $B = (0, 6)$. Compute side lengths $|OA|, |OB|, |AB|$. The incentre formula: $I = (a \cdot x_O + b \cdot x_A + c \cdot x_B)/(a + b + c)$ where $a, b, c$ are the sides opposite to the respective vertices.
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Correct Answer: (2)