Question

what is the radius of incircle of the right triangle with lengths of perpendicular sides 6 and 8

Answer 1

Step-by-step explanation:

ANSWER

Since AB,BC and CA are tangents to the circle

⇒ OP,OM and ON are radius of the incircle

To find : radius 'r' of the incircle.

ABC is a right angled triangle

AB

2

+AC

2

=BC

2

(Using pythagoras theorem)

⇒ (6)

2

+(8)

2

=BC

2

⇒ BC

2

=36+64

=100

⇒ BC=

100

=10cm

Since area of right anged triangle =

2

1

×base×height

⇒ Area of △ABC=

2

1

×6×8

=3×8=24cm

2

⇒ Area of △ABC=24cm

2

....(1)

Also, Area of △ABC= area of △OAC+ area of △OBC+ area of △OBA

=

2

1

×r×8+

2

1

×r×10+

2

1

×6×r=

2

1

r(8+10+6)=

2

1

r(24)=12r....(2)

Equating (1) and (2) 12r=24

⇒ r=

12

24

=2cm