Question

A circle of radius r has been incribed in a triangle of area ∆ . if the semiperimeter of the triangle be s, prove that r=∆/s.​

Answer 1

Answer:

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

1. s=
2. 2
3. 8+15+17
5. =
6. 2
7. 40
9. =20
10. ⇒r=
11. s
12. Δ
14. =
15. 20
16. 60
18. =3cm