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For any triangle ABC, ((a+b+c)(b+c-a)(c...

For any triangle ABC,
`((a+b+c)(b+c-a)(c+a-b)(a+b-c))/(4b^2c^2)`is equal to

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`((a + b + c) (b + c -a) (c + a - b) (a + b -c))/(4b^(2) c^(2))`
`= (2s 2 (s - a) 2 (s -b) 2 (s -c))/(4b^(2) c^(2))`
`= (4 Delta ^(2))/(b^(2) c^(2))`
`= (4)/(b^(2) c^(2)) ((1)/(2) bc sin A)^(2) = sin^(2) A`
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CENGAGE PUBLICATION-PROPERTIES AND SOLUTIONS OF TRIANGLE-Illustration
  1. Find the value of tan A, if area of Delta ABC is a^(2) -(b-c)^(2).

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  2. Prove that a^(2) sin 2B + b^(2) sin 2A = 4 Delta

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  3. For any triangle ABC, ((a+b+c)(b+c-a)(c+a-b)(a+b-c))/(4b^2c^2)is equa...

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  4. If the sides of a triangle are 17 , 25a n d28 , then find the greatest...

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  5. In equilateral triangle ABC with interior point D, if the perpendicula...

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  6. If area of a triangle is 2 sq. units, then find the value of the pr...

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  7. A triangle has sides 6,7, and 8. The line through its incenter para...

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  8. Each side of triangle ABC is divided into three equal parts. Find the ...

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  9. The two adjacent sides of a cyclic quadrilateral are 2and 5 and the an...

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  10. In triangle A B C ,a : b : c=4:5: 6. The ratio of the radius of the ci...

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  11. Given a triangle A B C with sides a=7, b=8 and c=5. Find the value of ...

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  12. If b=3,c=4,a n dB=pi/3, then find the number of triangles that can be ...

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  13. If A=30^0, a=7,and b=8 in A B C , then find the number of triangles t...

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  14. If in triangle ABC, (a=(1+sqrt(3))c m ,b=2c m ,a n d/C=60^0 , then fin...

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  15. In A B C , sides b , c and angle B are given such that a has two val...

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  16. In A B C ,a , ca n dA are given and b1,b2 are two values of the third...

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  17. O is the circumcenter of A B Ca n dR1, R2, R3 are respectively, the r...

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  18. In A B C ,C=60^0a n dB=45^0dot Line joining vertex A of triangle and ...

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  19. The diameters of the circumcirle of triangle ABC drawn from A,B and C ...

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  20. Find the lengths of chords of the circumcircle of triangle ABC, made b...

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