In a triangle ABC,if r_1 r_2 + r_3 r = 35,r_2 | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) Given equations: $r_1 r_2 + r_3 r = 35$,$r_2 r_3 + r r_1 = 63$,and $r_3 r_1 + r r_2 = 45$. Using the identities $r_1 = \frac{\Delta}{s-a}$,$r_2 =

Vedclass · Accepted Answer

$21$

Vedclass · Answer

(C) Given equations: $r_1 r_2 + r_3 r = 35$,$r_2 r_3 + r r_1 = 63$,and $r_3 r_1 + r r_2 = 45$. Using the identities $r_1 = \frac{\Delta}{s-a}$,$r_2 = \frac{\Delta}{s-b}$,$r_3 = \frac{\Delta}{s-c}$,and $r = \frac{\Delta}{s}$,we know that $r_1 r_2 + r_3 r = ab$,$r_2 r_3 + r r_1 = bc$,and $r_3 r_1 + r r_2 = ac$. Thus,$ab = 35$,$bc = 63$,and $ac = 45$. Multiplying these gives $(abc)^2 = 35 	imes 63 	imes 45 = 99225$,so $abc = 315$. Then $c = \frac{abc}{ab} = \frac{315}{35} = 9$,$a = \frac{abc}{bc} = \frac{315}{63} = 5$,and $b = \frac{abc}{ac} = \frac{315}{45} = 7$. Therefore,$2s = a + b + c = 5 + 7 + 9 = 21$.

In a triangle $ABC$,if $r_1 r_2 + r_3 r = 35$,$r_2 r_3 + r r_1 = 63$,and $r_3 r_1 + r r_2 = 45$,then $2s =$

Similar Questions

If $S$ is the circumcentre of a triangle $ABC$,$a=5, b=6, c=9$ and $SB=\frac{27}{4 \sqrt{2}}$,then $\sin 2C=$

If a triangle has sides $a, b, c$ and $r_1 > r_2 > r_3$ (where $r_1, r_2, r_3$ are the ex-radii),then:

In a triangle $ABC$ with usual notations,if $a=13, b=14, c=15$,then $\sin A=$

In any triangle $ABC$,if $a: b: c = 2: 3: 4$,then $R: r =$

In a triangle $ABC$,with usual notations,if $\frac{b+c}{11}=\frac{c+a}{12}=\frac{a+b}{13}$,then $\cos A : \cos B : \cos C =$

Vedclass Test Series

Exam Paper Generator

Online Exam Module