Question

16. ABC is a right A
angled triangle
with AB = 12 cm
and AC = 13 cm.
A circle, with
centre O, has been
inscribed inside
the triangle.
B01
Calculate the value of x, the radius ​

Answer 1

Answer:

THIS IS THE CORRECT ANSWER AND MARK THIS ANSWER AS BRAINLIEST ANSWER

Step-by-step explanation:

In △ABC,

⇒  ∠B=90o             [ Given ]

⇒  AB=12cm and AC=13cm           [ Given ]

Here, O is center of a circle and x is a radius.

⇒  (AC)2=(AB)2+(BC)2               [ By Pythagoras theorem ]

⇒  (13)2=(12)2+(BC)2

⇒  169=144+(BC)2

⇒  (BC)2=25

∴  BC=5cm

Now, AB,BC and CA are tangents to the circle at P,N and M respectively.

∴  OP=ON=OM=x          [ Radius of a circle ]

⇒  Area of △ABC=21×BC×AB

                                 

                                  =21×5×12

                                  =30cm2

Area of △ABC= Area of △OAB+ Area of △OBC+ Area of △OCA

⇒  30=21x×AB+21