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CAT 2024 Slot 2 QA Question & Solution

GeometryMedium

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

Solution

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

image

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 $\frac{1}{2}\times\ 6\times\ 8=24$
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.