If- in - ABC- r3-r1-r2-r- then - A- B-

Given, r_3=r_1+r_2+r, ⇒ r_1+r_2=r_3 r ⇒Δ (s a)+Δ (s b )=Δ (s c) nbsp; Δs ⇒Δ(2s a b(s a)(s b))=Δ(cs(s c)) ⇒c(s a)(s b)=cs(s c) ⇒ s^2 cs=s^2 bs as+ab ⇒ s(a+b c ...

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Byju's Answer

Standard VIII

Mathematics

Properties of Angles Formed by Two Parallel Lines and a Transversal

If, in Δ ABC,...

Question

If, in $Δ A B C, r_{3} = r_{1} + r_{2} + r,$ then $∠ A + ∠ B =$

120^{\circ}

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60^{\circ}

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90^{\circ}

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45^{\circ}

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Solution

The correct option is C $90^{\circ}$
Given, $r_{3} = r_{1} + r_{2} + r,$
$\Rightarrow r_{1} + r_{2} = r_{3} - r$
$\Rightarrow \frac{Δ}{(s - a)} + \frac{Δ}{(s - b)} = \frac{Δ}{(s - c)} - \frac{Δ}{s}$
$\Rightarrow Δ (\frac{2 s - a - b}{(s - a) (s - b)}) = Δ (\frac{c}{s (s - c)})$
$\Rightarrow \frac{c}{(s - a) (s - b)} = \frac{c}{s (s - c)}$
$\Rightarrow s^{2} - c s = s^{2} - b s - a s + a b$
$\Rightarrow s (a + b - c) = a b$
$\Rightarrow (a + b + c) (a + b - c) = 2 a b$
$\Rightarrow (a + b)^{2} - c^{2} = 2 a b$
$\Rightarrow a^{2} + b^{2} = c^{2}$
$\Rightarrow ∠ C = 90^{\circ}$
$\Rightarrow ∠ A + ∠ B = 90^{\circ}$

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If, in ΔABC, r3=r1+r2+r, then ∠A+∠B=

If, in $Δ A B C, r_{3} = r_{1} + r_{2} + r,$ then $∠ A + ∠ B =$