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

Answer 1

Correct Answer: 2

The given triangle is a right-angled triangle with side lengths: 6 units, 8 units, and 10 units. 

Since it's a right triangle, we can use the formula for the inradius \( r \) of a right-angled triangle:

\[ r = \frac{a + b - c}{2} \] where \( a \) and \( b \) are the legs, and \( c \) is the hypotenuse.

Substituting the values: \( a = 6 \), \( b = 8 \), and \( c = 10 \), we get:

\[ r = \frac{6 + 8 - 10}{2} = \frac{4}{2} = 2 \]

Therefore, the radius of the incircle is 2 units.