1.

triangle ABC is a right angled triangle with AB = 12cm and AC = 13cm. A circle with centre O has been inscribed inside the triangle. calculate the radius of the inscribed circle​

Answer»

Step-by-step explanation:

In △ABC,

⇒ ∠B=90

o

[ 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=

2

1

×BC×AB

=

2

1

×5×12

=30cm

2

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

⇒ 30=

2

1

x×AB+

2

1

x×BC+

2

1

x×CA

⇒ 30=

2

1

x(AB+BC+CA)

⇒ x=

AB+BC+CA

2×30

⇒ x=

12+5+13

60

⇒ x=

30

60

∴ x=2cm



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