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The sides of a right triangle ABC are a, b and c, where c is the hypotenuse. What will be the radius of the in circle of this triangle?
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(a + b + c) 2 -
(a + b - c) 2 -
(b - c + a) 2 -
(a + c - b) 2
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Correct Option: B
As per the given in question , we draw a figure right-angled triangle ACB 
In radius = r units
Area of (∆OAC + ∆OBC + ∆OAB) = Area of ∆ABC
| ⇒ | br + | ar + | cr = | ab | ||||
| 2 | 2 | 2 | 2 |
r (a + b + c) = ab
| ⇒ r = | . . . . . (i) | |
| a + b + c |
In right angled triangle ∆ABC,
a² + b² = c²
⇒ (a + b)² – 2ab = c²
⇒ (a + b)² – c² = 2ab
⇒ (a + b + c) (a + b – c) = 2ab
∴ From equation (i),
| r = | |
| a + b + c |
| r = | |
| 2(a + b + c) |
| r = | |
| 2 |
