# If one of the sides of a right angled triangle, whose all sides have integral values, is #12#, then what is the largest possible radius of its incircle?

##
A. #3#

B. #4#

C. #6#

D. #5#

A.

B.

C.

D.

##### 1 Answer

#### Answer:

Answer is **D**.

#### Explanation:

Incircle in a right angled triangle is very special case. Infact it can be proved easily using the following figure (by joining incenter to the vertices of the triangle).

that radius of incircle is

As one of the side is

Further if all sides are integers if

Possible solutions are

and for these we get

Hence, largest incircle possible is of radius **D**.