Question

26. In a right triangle ABC, right angled at B, BC= 15cm and AB=8cm. A circle is inscribed in triangle
ABC. Find the radius of the circle.
2M​

Answer 1

Step-by-step explanation:

Using Pythagoras theorem in △ABC

(AB)

2

+(BC)

2

=(AC)

2

(15)

2

+(8)

2

=(AC)

2

⇒(AC)

2

=225+64=289

⇒AC=17cm

Now inradius r=

s

Δ

where Δ is the area of triangle and s is semi perimeter.

Δ=

2

1

×8×15=60

s=

2

8+15+17

=

2

40

=20

⇒r=

s

Δ

=

20

60

=3cm

Answer 2

Step-by-step explanation:

Using Pythagoras theorem in  triangleABC, we get

AC^2= 8^2 + 15^2= 289

AC= root289= 17

radius of circle inscribed in triangle ABC = Area of triangle / semi perimeter of triangle ABC

ar. of triangle = 1/2 ×base ×height = 1/2×8×15= 60

semi perimeter of triangle= AB+BC+AC/2= 17+8+15/2= 40/2= 20

r=60/20=3

HOPE YOU WILL GET YOUR ANSWER