cat 2024 Question 2

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

Upon drawing a rough sketch of the coordinates given, we realise that this is a right-angled triangle.

The three side lengths are 6, 8 and 10 units

The inradius of a circle can be calculated using the formula: $rs=Area$, where s is the semi-perimeter of the triangle

The Area would be $\frac{1}{2} imes\ 6 imes\ 8=24$

and the semi-perimeter would be $\frac{10+6+8}{2}=12$

Giving the inradius to be $\frac{24}{12}=2$ units

Therefore, 2 is the correct answer.

Question 2.