Question

A triangle has corners at `(9 , 2 )`, `(4 ,7 )`, and `(5 ,6 )`. What is the radius of the triangle's inscribed circle?

Answer 1

The three points lie on a single straight line, so they are collinear and do not form a triangle.

Explanation:

Given `A(4,7), B(5,6) and C(9,2)`,

`m_(AB)=(6-7)/(5-4)=-1`

`m_(BC)=(2-6)/(9-5)=-1`

As the two segments `AB` and `BC` have a same gradient of `-1` and a common point `B`, the three points `A,B and C` are collinear.