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In a triangle ABC, if a=4,b=8,/C=60^@, t...

In a triangle ABC, if `a=4,b=8,/_C=60^@`, then which of the following relations is (are) correct? [Note: All symbols used have usual meaning in triangle ABC.]

A

(a)The area of `Delta ABC is 8sqrt3`

B

(b)The value of `sum sin ^(2)A=2`

C

(c)Inradius of trianlgle `ABC is (2sqrt3)/(3+sqrt3)`

D

(d)The length of internal angle bisector of `angle C is (4)/(sqrt3).`

Text Solution

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The correct Answer is:
A, B
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ARIHANT MATHS ENGLISH-PROPERTIES AND SOLUTION OF TRIANGLES -Exercise (More Than One Correct Option Type Questions)
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  2. If in DeltaABC, a = 5, b = 4 and cos (A - B) = 31/32, then

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  3. In which of the following situations, it is possible to have a DeltaAB...

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  4. In a triangle ABC, let BC = 1, AC=2 and measure of / C is 30^@. Which ...

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  5. Let one angle of a triangle be 60°, the area of triangle is 10sqrt3and...

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  6. In a triangle ABC, if a=4,b=8,/C=60^@, then which of the following rel...

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  8. There can exist a triangle ABC satisfying the conditions :

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  9. Let a,b,c be the sides of triangle whose perimeter is P and area is A,...

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  10. If in DeltaABC, A =90^(@) and c, sin B and cos B are rational number, ...

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  11. Let 'l' is the length of median from the vertex A to the side BC of a ...

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  12. If A,A1,A2 and A3 are the areas of the inscribed and escribed circles ...

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  13. If a, b, A be given in a triangle and c1 and c2 be two possible value ...

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  14. D,E and F are the middle points of the sides of the triangle ABC, then

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  15. The sides of A B C satisfy the equation 2a^2+4b^2+c^2=4a b+2ac Then a...

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  16. If Delta represents the area of acute angled triangle ABC, then sqrt(a...

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  17. In triangle, A B Cif2a^2b^2+2b^2c^2=a^2+b^4+c^4, then angle B is equal...

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  18. If H is the orthocentre of triangle ABC, R = circumradius and P = AH +...

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  19. If inside a big circle exactly n(nlt=3) small circles, each of radius ...

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