JEE Main 2022 · 25 Jun · Shift 1 · Mathematics Q3

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MathematicsSingle correct+4 / -1Question 3 of 90

Let a, b and c be the length of sides of a triangle ABC such that $\dfrac{a+b}7=\dfrac{b+c}8=\dfrac{c+a}9$ . If r and R are the radius of incircle and radius of circumcircle of the triangle ABC, respectively, then the value of $\dfrac Rr$ is equal to :

\dfrac52

\dfrac32

Answer and worked solution

Official answer: A

Sides. Put $a+b=7k$ , $b+c=8k$ , $c+a=9k$ ; then $a+b+c=12k$ , so $a=4k$ , $b=3k$ , $c=5k$ .

Right triangle (3 : 4 : 5): $R=\dfrac{5k}2$ and $r=\dfrac{3k+4k-5k}2=k$ .

Ratio. $\dfrac Rr=\dfrac52$ .

(A)

Topics:Properties of triangles

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JEE Main 2022 · 25 Jun · Shift 1, Mathematics question 3