In a triangle ABC- if b - c -2 a and - A -600- then - ABC isA- equilateralB- isoscelesC- right angledD- scalene

The correct option is A equilateral ∵∠ A+ ∠ B+ ∠ C=180^0 ∴∠ B+∠ C=120^0 b+c=2a ⇒ sin B+sin C=2sin 60^0 ⇒ 2sin B+C/2cos B C/2=2 √(3)/2 2 sin 60^0 cosB C/2=1 ⇒ ...

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Byju's Answer

Standard IX

Mathematics

Every Point on the Bisector of an Angle Is Equidistant from the Sides of the Angle.

In a triangle...

Question

In a triangle ABC, if b + c = 2a and $∠$ $A = 60^{0}$ , then $Δ$ ABC is

equilateral

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right angled

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isosceles

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scalene

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Solution

The correct option is A
equilateral

$∵ ∠ A + ∠ B + ∠ C = 180^{0} ∴ ∠ B + ∠ C = 120^{0} b + c = 2 a \Rightarrow s i n B + s i n C = 2 s i n 60^{0} \Rightarrow 2 s i n \frac{B + C}{2} c o s \frac{B - C}{2} = \frac{2 \sqrt{3}}{2} 2 s i n 60^{0} c o s \frac{B - C}{2} = 1 \Rightarrow \frac{B - C}{2} = 0 \Rightarrow ∠ B = ∠ C ∴ ∠ A = ∠ B = ∠ C \Rightarrow Δ i s e q u i l a t e r a l .$

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In a triangle ABC, if b + c = 2a and ∠ A=600, then Δ ABC is

The correct option is A equilateral ∵∠A+∠B+∠C=1800∴∠B+∠C=1200b+c=2a⇒sin B+sin C=2sin 600⇒2sinB+C2cosB−C2=2√322 sin 600 cosB−C2=1⇒B−C2=0⇒∠B=∠C∴∠A=∠B=∠C⇒Δ is equilateral.

In a triangle ABC, if b + c = 2a and $∠$ $A = 60^{0}$ , then $Δ$ ABC is