Question

In triangle, ABC, B = 90°. A circle touches all
the sides of A ABC. If AB + AC = 32 cm and
BC = 24 cm, find the radius of the incircle
of triangle ABC.​

Answer 1

Step-by-step explanation:

if O ’ is the center of smaller circle OO′C are co-linear. If H is the point of tangency of smaller circle with AC . OO′=5 (sum of the two radii.DH should be 52−(4–1)2−−−−−−−−−√=4.

△ODC ∼△O′HC.

DCHC=41 So DHHC=31 i.e. HC=43

Taking AE = AD = x

We have Pythagoras theorem,

AB = x + 4 ; BC = 4 + 4 + 43 ; AC = x + 4 + 43

AB2 + BC2 = AC2 ; This leads to x = 28

AB = 28 + 4 = 32

>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>

The above one was too long. shorer solution is possible.

sinθ = 35 ⟹ tanθ = 34

FC = 4 tanθ = 163

BC = 4 + FC = 283

∠C = 2θ ; tan2θ = 2 tanθ1 − tan2θ = 247

AB=BC ∗ tan2θ = 32....

Answer 2

Step-by-step explanation:

ab=ac *ac= 32

the radius of triangle abc