# ABC is a Right Triangle ,right angled at B. C(o,r) is the incircle and o is the incenter of the triangle.AB=5,BC=12,what is the radius of incircle?

May 17, 2018

Radius of the incircle is $2.0$ unit

#### Explanation:

In Right Triangle the legs are $A B = P = 5 , B C = B = 12$

Then hypotenuse is $H = \sqrt{{P}^{2} + {B}^{2}} = \sqrt{25 + 144} = 13$

In Right Triangle incircle radius is

$r = \frac{P + B - H}{2} = \frac{5 + 12 - 13}{2} = 2.0$

Radius of the incircle is $2.0$ unit [Ans]

May 17, 2018

$2$.

#### Explanation:

Observe that, the hypotenuse $A C = 13$.

From Trigonometry, we know that, $\Delta = r s$.

Here, $\Delta = \text{the Area of the triangle ABC}$,

$= \frac{1}{2} \cdot A B \cdot B C$,

$= \frac{1}{2} \cdot 5 \cdot 12$,

$= 30$,

$r = \text{the inradius, and, }$

$s = \text{semi-perimeter}$,

$= \frac{1}{2} \left(A B + B C + A C\right)$,

$= \frac{1}{2} \left(5 + 12 + 13\right)$,

$15$.

$\therefore r = \frac{\Delta}{s}$,

$= \frac{30}{15}$,

$= 2$,

as Respected Binayaka C. has readily derived!