Home
Class 12
MATHS
Statement-1: In any !ABC, if a : b : c =...

Statement-1: In any `!ABC`, if a : b : c = 4 : 5 : 6, then R:r=16:17.
Statement-2: In any `!ABC,R/r=(abc)/(4s)`

A

Statement-1 is True, Statement-2 is true, Statement-2 is a correct explanation for Statement-1.

B

Statement-1 is True, Statement-2 is True, Statement-2 is not a correct explanation for Statement-1.

C

Statement-1 is True, Statement-2 is False.

D

Statement-1 is False, Statement- 2 is True.

Text Solution

Verified by Experts

Statement-2 is not true as
`R/r=(abc)/(4!)xxs/(!)=(abcs)/(4!^(2))`
If a : b : c = 4 : 5 : 6, then
a=4x,b=5x andc=6x and `s=(15x)/2`
`thereforeR/r=(abcs)/(4!^(2))=(abc)/(4(s-a)(s-b)(s-c))`
`rArrR/r=(abcs)/(4!^(2))=(120x^(3))/(4xx(7x)/2xx(5x)/2xx(3x)/2)=16/7`
So, statement-! is true.
Promotional Banner

Topper's Solved these Questions

  • PROPERTIES OF TRIANGLES AND CIRCLES CONNECTED WITH THEM

    OBJECTIVE RD SHARMA|Exercise Exercise|98 Videos

  • PROPERTIES OF TRIANGLES AND CIRCLES CONNECTED WITH THEM

    OBJECTIVE RD SHARMA|Exercise Chapter Test|55 Videos

  • PROPERTIES OF TRIANGLES AND CIRCLES CONNECTED WITH THEM

    OBJECTIVE RD SHARMA|Exercise SOLVED MCQ|2 Videos

  • PLANE AND STRAIGHT LINE IN SPACE

    OBJECTIVE RD SHARMA|Exercise Chapter Test|31 Videos

  • REAL FUNCTIONS

    OBJECTIVE RD SHARMA|Exercise Chapter Test|60 Videos

Similar Questions

Explore conceptually related problems

Statement 1. In a triangle ABC, if a:b:c=4:5:6, then R:r=16:7 , Statement 2. In a triangle ABC, R:r=abc:4s (A) Both Statement 1 and Statement 2 are true and Statement 2 is the correct explanation of Statement 1 (B) Both Statement 1 and Statement 2 are true and Statement 2 is not the correct explanatioin of Statement 1 (C) Statement 1 is true but Statement 2 is false. (D) Statement 1 is false but Stastement 2 is true

Statement-1: In any !ABC , a cos A + b cos B + c cos C le s Statement-2 : In any !ABC,sinA/2sinB/2sinC/2le1/8

In a !ABC , if 2R + r = r_(1) , then

In a !ABC if r_(1):r_(2):r_(3)=2:4:6, then a:b:c =

In a triangle ABC, if a:b:C=3:7:8, then R:r is equal to

In a !ABC , if r_(1) =2r_(2) =3r_(3) , then a:b:c =

In a !ABC if r_(1) = 8, r_(2) = 12 and r_(3) = 24, then a =

In a trianlge ABC if A=90^(@), b =3 and c=4 then R : r is

Statement-1: ln !ABC,r_(1)+r_(2)+r_(3)-r=4R Statement-2: In !ABC,r_(1)r_(2)+r_(2)r_(3)+r_(3)r_(1)=!^(2)

In triangle ABC, if cos A + cos B + cos C = (7)/(4), " then " (R)/(r) is equal to