In the given figure, if in a right triangle ABC, right-angled at B, BC=12 cm and AB=5 cm, then which of the following is the radius of the circle inscribed in the triangle?

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1 cm

2 cm

3 cm

4 cm

answer is B.

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Detailed Solution

Consider the given figure,
Question Image

Given that,
BC=12 cm.
AB=5 cm.
We know that according to Pythagoras theorem,

h y p o t e n u s e 2 = b a s e 2 + p e r p e n d i c u l a r 2

Using Pythagoras theorem in ∆ABC,
Question Image

Let us consider the radius as

x

cm.
From figure,

Hence, the radius of the circle inscribed in the triangle is

2 cm

.
Therefore, option 2 is correct.

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