Question

In fig. (1), abc is a triangle in which b = 90º, bc = 48 cm and ab = 14 cm. A circle is inscribed in the triangle, whose centre is o. Find radius r of in-circle.

Answer 1

Answer:  6 cm

Step-by-step explanation:

Since, we know that,

In right angle triangle that having sides a, b and c ( where c is the hypotenuse)

The radius of in circle, $r = \frac{a+b-c}{2}$

Here, In triangle ABC,

AB = 14 cm , BC = 48 cm and ∠B = 90°

Thus, By Pythagoras theorem,

$AC^2 = AB^2+BC^2$

⇒ $AC^2 = (14)^2+(48)^2$

⇒ $AC^2 = 196+2304$

⇒ $AC^2 = 2500$

⇒ AC = 50

Thus, the radius r of in circle,

$\frac{AB+BC-AC}{2} = \frac{14+48-50}{2} = \frac{12}{2} = 6$

⇒ r = 6 cm

Answer 2

Answer:

6 cm

Step-by-step explanation: