In a △ABC, with usual notation, if r=r1−r2−r3, then 2R=
Topic: JEE PYQ
Answer: A. Full step-by-step solution below.
Aa
Bb+c
Cc
Dc+a
Correct answer: A
Solution
(a) In a △ABC, it is given that, r=r1−r2−r3⇒sΔ=s−aΔ−s−bΔ−s−cΔ⇒s−b1+s−c1=s−a1−s1⇒(s−b)(s−c)2s−b−c=s(s−a)a⇒s(s−a)=s2−(b+c)s+bc⇒s2−sa=s2−(b+c)s+bc⇒(b+c−a)s=bc⇒(b+c)2−a2=2bc⇒b2+c2+2bc−a2=2bc⇒b2+c2=a2 ∴△ABC is the right-angled triangle with angle A=90∘,so2R=a.