SSC CHSL Model Paper 19

Question : 61 of 99

Marks: +1, -0

The sides of a right angled triangle ABC are a, b and c, where c is the hypotenuse. What will be the radius of the in-circle of this triangle?

Solution:

In radius = r units
Area of (ΔOAC + ΔOBC + ΔOAB) = Area of ΔABC
⇒

1/2br+1/2ar+1/2cr

=1/2ab

r(a+b+c) = ab

⇒

r={ab}/(a+b+c)

......(i)
In right angled triangle ΔABC,

a^2 + b^2 = c^2

⇒

(a + b)^2 - 2ab = c^2

⇒

(a + b)^2 - c^2 = 2ab

⇒

(a + b + c) [a + b - c) = 2ab

∴ From equation (i).

r={ab}/(a+b+c)

{(a+b + c) (a+ b-c)}/{2 (a + b + c)}

=(a + b -c)/2

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