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Exterior Angle Property

In Δ ABC ...

Question

In $Δ$ $A B C$ the sides opposite to angles $A, B, C$ are denoted by $a, b, c$ respectively.
If $a^{2} + b^{2} + c^{2} = 8 R^{2},$ where $R =$ circumradius, then the triangle is?

equilateral

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isosceles

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right angled

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none of these

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Solution

The correct option is C right angled
we know that
$a = 2 R s i n A b = 2 R s i n B c = 2 R s i n C$

when, $b = 90^{o}, a = c = 45^{o}$

do, $a = \sqrt{2} R, b = 2 R, c = \sqrt{2} R$

Now,, $a^{2} + b^{2} + c^{2} = (4 + 2 + 2) R^{2} = 8 R^{2}$

Therefore, the Triangle must be Right Angled to satisfy given condition.

So, Correct Answer is $C$

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Similar questions

Δ

A B C

the sides opposite to angles

A, B, C

are denoted by

a, b, c

respectively.

Let

a^{2} + b^{2} = c^{2}

. If

R

and

r

are its circumradius and inradius respectively then

R + r

is equal to?

Δ

A B C

the sides opposite to angles

A, B, C

are denoted by

a, b, c

respectively.

C = 90^{o}

, then

\frac{a^{2} + b^{2}}{a^{2} - b^{2}} sin (A - B) = ?

Δ

A B C

the sides opposite to angles

A, B, C

are denoted by

a, b, c

respectively.

a^{2} + c^{2} = 2002 b^{2},

then

\frac{cot A + cot C}{cot B}

is equal to

Δ

A B C

the sides opposite to angles

A, B, C

are denoted by

a, b, c

respectively.

If the area of a triangle

A B C

is given by

Δ = a^{2} - (b - c)^{2}

, then

tan A

is equal to?

Δ

A B C

the sides opposite to angles

A, B, C

are denoted by

a, b, c

respectively.

a^{2}

b^{2}

c^{2}

are in A.P., then

tan A

tan B

tan C

are in?

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In Δ ABC the sides opposite to angles A,B,C are denoted by a,b,c respectively.If a2+b2+c2=8R2, where R= circumradius, then the triangle is?

The correct option is C right angledwe know thata=2RsinAb=2RsinBc=2RsinCwhen, b=90o,a=c=45odo,a=√2R,b=2R,c=√2RNow,, a2+b2+c2=(4+2+2)R2=8R2Therefore, the Triangle must be Right Angled to satisfy given condition.So, Correct Answer is C

In $Δ$ $A B C$ the sides opposite to angles $A, B, C$ are denoted by $a, b, c$ respectively.
If $a^{2} + b^{2} + c^{2} = 8 R^{2},$ where $R =$ circumradius, then the triangle is?