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

2. Let vertices be $A(1,2)$, $B(7,2)$, and $C(1,10)$. - $AC$ is vertical of length $|10 - 2| = 8$. - $AB$ is horizontal of length $|7 - 1| = 6$. Since $AC$ is vertical and $AB$ is horizontal, $\angle A = 90^\circ$. So $	riangle ABC$ is a right-angled triangle with perpendicular sides $a = 6$ and $b = 8$. Hypotenuse $c = \sqrt{6^2 + 8^2} = 10$. Inradius $r = \frac{a + b - c}{2} = \frac{6 + 8 - 10}{2} = 2$.

Incircle Radius of Triangle

Explanation

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