A right angled triangle abc is right angled at
b. The point of contact of the incircle with the hypotenuse, divides it, in the ratio 3:2. If the perimeter of the triangle is 36 cm, find the inradius
Answers
Solution :-
we know that,
- Inradius of right angled ∆ = (P + B - H)/2 .
given ,
- Perimeter = P + B + H = 36 cm .
so,
→ Inradius = (P + B - H)/2
→ Inradius = {(P + B + H) - 2H} / 2
→ Inradius = (36 - 2H)/2
→ Inradius = (18 - H)
now, let hypotenuse is equal to 3x + 2x = 5x cm .
then, P and H must be ,
- 3x and 4x respectively .
so,
→ 3x + 4x + 5x = 36
→ 12x = 36
→ x = 3 .
therefore,
→ H = 5x = 3 * 5 = 15 cm.
hence,
→ Inradius = 18 - H = 18 - 15 = 3 cm. (Ans.)
∴ the inradius of the given right angled triangle will be 3 cm.
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Answer:
3
Step-by-step explanation:
If ABC is a right angled triangle and right angled triangle at B, an incircle is drawn then circle touches the sides AC at D, AB at E, BC at F. Let ' r ' be the radius of the incircle and ' o ' be the center of incircle. A square BFOE is formed with all sides equal ' r '.
Given that The point of contact of the incircle with the hypotenuse, divides it, in the ratio 3:2
=> AD : DC = 3:2
Since the tangents to the circle are equal AD = AE = 3x
similarly, DC = FC = 2x.
Therefore, AB = 3x+r ; BC = 2x+r ; AC = 5x.
Given that perimeter of = 36
=> 3x+r+2x+r+5x =36
=> By simplifying 5x+r = 18
If the sides of a right angled triangle are 3, 4, 5 ( By Pythagoras theorem) then x = r, then we get r = 3