Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app

BITSAT 2011

Exam: BITSAT
Year: 2011
Subject: Mathematics
Chapter: Properties of Triangles

BITSAT 2011 · Mathematics · Properties of Triangles

In an equilateral triangle, the in radius, circumradius and one of...

In an equilateral triangle, the in radius, circumradius and one of the ex-radii are in the ratio

Options

A $2: 3: 5$
B $1: 2: 3$
C $3: 7: 9$
D $3: 7: 9$

Correct answer

B. $1: 2: 3$

Step-by-step solution

We have (

\Delta=\frac{\sqrt{3}}{4} \mathrm{a}^

2,

\mathrm{~s}=\frac{3 \mathrm{a}}{2}

) (\therefore \quad r=

\frac{\Delta}{\mathrm{s}}=\frac{\mathrm{a}}{2 \sqrt{3}}, \mathrm{R}=\frac{\mathrm{abc}}{4 \Delta}=\frac{\mathrm{a}^3}{\sqrt{3} \mathrm{a}^2}=\frac{\mathrm{a}}{\sqrt{3}}

) and (r_1=

\frac{\Delta}{s-a}=\frac{\sqrt{3} / 4 a^2}{a / 2}=\frac{\sqrt{3}}{2}

a) Hence, (

\mathrm{r}

:

\mathrm{R}

: \m

mathrm{r}}_{1}=\frac{\mathrm{a}

}{2

\sqrt{3}

}:

\frac{\mathrm{a}}{\sqrt{3}}

:

\frac{\sqrt{3}}{2} \mathrm{a}=

1: 2: 3)

Practice Properties of Triangles on Quantrex Academy →

More from Properties of Triangles

If in a A B C, 2 b^2=a^2+c^2 , then ( 3B)/( B) is equal to BITSAT 2022 Let ABC be an acute-angled triangle and let D be the mid-point of BC . If AB = AD , then… BITSAT 2019 In a ABC, if A a = B b = C c , and the side a=2, then area of the triangle is BITSAT 2016 In a A B C , the lengths of the two larger sides are 10 and 9 units, respectively. If the… BITSAT 2015 In a triangle ABC, if a=2, B=60^ ^ ∘ and C=75^ ^ ∘ , then b equals BITSAT 2012 The random variable X has the following probability distribution x 0 1 2 3 4 P(X=x) k 3 k… BITSAT 2009 Full Properties of Triangles list Properties of Triangles JEE Maths PYQs JEE Mathematics PYQs All BITSAT PYQs