Home
Class 12
MATHS
In triangle A B C ,a : b : c=4:5: 6. The...

In triangle `A B C ,a : b : c=4:5: 6.` The ratio of the radius of the circumcircle to that of the incircle is____.

Text Solution

Verified by Experts

`a = 4k, b = 5k, c = 6k`
`s = (15)/(2) k`,
`s - a = (7)/(2) k`,
`s - b = (5)/(2) k`,
`s - c = (3)/(2) k`
`rArr Delta^(2) = 15 xx 7 xx 5 xx 3 ((k)/(2))^(4)`
or `Delta = 15 sqrt7 ((k)/(2))^(2)`
Now, `r = (Delta)/(s) = (15 sqrt7 (k//2)^(2))/((15//2) k) = sqrt7 (k)/(2)`
and `R = (abc)/(4 Delta) = (4 xx 5 xx 6 xx k^(3))/(4 xx 15 sqrt7 xx (k^(2)//4)) = (8)/(sqrt7) k`
`:. (R)/(r) = (16)/(7)`
Promotional Banner

Topper's Solved these Questions

  • PROPERTIES AND SOLUTIONS OF TRIANGLE

    CENGAGE|Exercise Exercise 5.1|12 Videos

  • PROPERTIES AND SOLUTIONS OF TRIANGLE

    CENGAGE|Exercise Exercise 5.2|8 Videos

  • PROGRESSION AND SERIES

    CENGAGE|Exercise ARCHIVES (MATRIX MATCH TYPE )|1 Videos

  • PROPERTIES OF TRIANGLE, HEIGHT AND DISTANCE

    CENGAGE|Exercise Question Bank|32 Videos

Similar Questions

Explore conceptually related problems

In triangle ABC,a:b:c=4:5:6. The ratio of the radius of the circumcircle to that of the incircle is

In a triangle ABC, AB = BC = CA. The ratio of the radius of the circumcircle to that of the incircle is

The ratio of the areas of the circumcircle and the incircle of a square is

The ratio of the areas of the circumcircle and the incircle of an equilateral triangle is

The ratio of the areas of the incircle and the circumcircle of a square is-

The ratio of the areas of the incircle and circumcircle of a square is

In a triangle ABC, prove that the ratio of the area of the incircle to that of the triangle is pi:cot((A)/(2))cot((B)/(2))cot((C)/(2))

Find the ratio of the areas of the incircle and circumcircle of a square.

In a triangle ABC if a: b: c= 4:5:6 then ratio between its circumradius and inredius is