Home
Class 12
MATHS
Given that Delta = 6, r(1) = 2,r(2)= 3,...

Given that `Delta = 6, r_(1) = 2,r_(2)= 3, r_(3) = 6`
Circumradius R is equal to a) 2.5 b)3.5 c)1.5 d)none of these

A

2.5

B

3.5

C

1.5

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
A
We have,
`r_(1) = (Delta)/(s-a) = 2, r_(2) = (Delta)/(s-b) = 3, r_(3) = (Delta)/(s-c) = 6`
Given `Delta =6`,
`:. S-a = 3` ...(i)
`s-b =2` ...(ii)
`s-c =1` ...(iii)
Adding Eqs. (i) and (ii), `2s - a - b =5 " or " a + b + c -a -b = 5 or c = 5`
Adding Eqs. (i) and (iii), `2s - a- c = 4, or b = 4`
And adding Eqs. (ii) and (iii), `2s -b -c = 3 or a = 3`
Hence the sides of the `Delta` are `a =3, b = 4, c = 5`
Since the triangle is right angled, the greatest angle is `90^(@)`.
Also, the least angle is opposite to side a, which is `sin^(-1).(3)/(5)`. Therefore,
`90^(@) - "sin"^(-1)(3)/(5) = "cos"^(-1)(3)/(5)`
Also, `R = (abc)/(4Delta) = (60)/(24) = 2.5`
`r = (Delta)/(s) = (6)/(6) = 1`
Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

  • PROPERTIES AND SOLUTIONS OF TRIANGLE

    CENGAGE PUBLICATION|Exercise Matrix match type|6 Videos

  • PROPERTIES AND SOLUTIONS OF TRIANGLE

    CENGAGE PUBLICATION|Exercise Numerical value type|22 Videos

  • PROPERTIES AND SOLUTIONS OF TRIANGLE

    CENGAGE PUBLICATION|Exercise Multiple correct answer type|24 Videos

  • PROGRESSION AND SERIES

    CENGAGE PUBLICATION|Exercise ARCHIVES (NUMERICAL VALUE TYPE )|8 Videos

  • RELATIONS AND FUNCTIONS

    CENGAGE PUBLICATION|Exercise All Questions|1119 Videos

Similar Questions

Explore conceptually related problems

Given that Delta = 6,r_1=2, r_(2) = 3, r_(3) = 6 then Inradius is equal to

In triangle ABC, if r_(1) = 2r_(2) = 3r_(3) , then b : c is equal to

Given that Delta = 6, r_(1) = 2,r_(2)=3, r_(3) = 6 Difference between the greatest and the least angles is

If in a triangle (r)/(r_(1)) = (r_(2))/(r_(3)) , then

In DeltaABC, R, r, r_(1), r_(2), r_(3) denote the circumradius, inradius, the exradii opposite to the vertices A,B, C respectively. Given that r_(1) :r_(2): r_(3) = 1: 2 : 3 The sides of the triangle are in the ratio

In any triangle, the minimum value of r^(3) /(r_(1) r_(2) r_(3)) is equal to

In triangle A B C , if r_1=2r_2=3r_3, then a : b is equal to 5/4 (b) 4/5 (c) 7/4 (d) 4/7

In Delta ABC , if r_(1) lt r_(2) lt r_(3) , then find the order of lengths of the sides

Prove that (r_(1) -r)/(a) + (r_(2) -r)/(b) = (c)/(r_(3))

Prove that r_(1) r_(2) + r_(2) r_(3) + r_(3) r_(1) = (1)/(4) (a + b + c)^(2)

Home
Profile