CAT 2024 Slot 2 QA Question 13: The coordinates of the three vertices of a triangle are: $(1, 2)$, $(7, 2)$, and $(1, 10)$. Then the radius of the incircle of the triangle is

Question

The coordinates of the three vertices of a triangle are: $(1, 2)$, $(7, 2)$, and $(1, 10)$. Then the radius of the incircle of the triangle is

Accepted Answer

The points $(1, 2)$ and $(7, 2)$ have the same y-coordinate, so their distance is $6$.
The points $(1, 2)$ and $(1, 10)$ have the same x-coordinate, so their distance is $8$.
Thus, the triangle is right-angled with legs $6$ and $8$, and hypotenuse $10$.
For a right triangle, inradius $r$ is:
$r = \d

The coordinates of the three vertices of a triangle are: (1,2)(1, 2)(1,2), (7,2)(7, 2)(7,2), and (1,10)(1, 10)(1,10). Then the radius of the incircle of the triangle is

The coordinates of the three vertices of a triangle are: $(1, 2)$ , $(7, 2)$ , and $(1, 10)$ . Then the radius of the incircle of the triangle is