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If c^(2) = a^(2) + b^(2), then prove tha...

If `c^(2) = a^(2) + b^(2)`, then prove that `4s (s - a) (s - b) (s - c) = a^(2) b^(2)`

A

`a^(2)b^(2)`

B

`c^(2)a^(2)`

C

`b^(2)c^(2)`

D

`s^(4)`

Text Solution

Verified by Experts

We have,
`c^(2)=a^(2)+b^(2)`
`rArrDelta` ABC is right triangle right-angled at C.
`therefore` Area of `DeltaABC=1/2absinC=1/2ab`
`rArrsqrt(s(s-a)(s-b)(s-c))=1/2ab`
`rArr4s(s-a)(s-b)(s-c)=a^(2)b^(2)`
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OBJECTIVE RD SHARMA ENGLISH-PROPERTIES OF TRIANGLES AND CIRCLES CONNECTED WITH THEM-Chapter Test
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  2. If the sides of a triangle are in the ratio 3 : 7 : 8, then find R : r

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  3. The area of a regular polygon of n sides is (where r is inradius, R is...

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  4. If the angles of a triangle are 30^(@) and 45^(@), and the included si...

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  5. In a DeltaABC, angleB=(pi)/(3) and angleC=(pi)/(4) let D divide BC in...

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  6. If A is the area and 2s is the sum of the sides of a triangle, then Al...

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  7. If in a triangle ABC, right angled at B, s-a=3, s-c=2, then the values...

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  8. If the sides of a triangle are a, b and sqrt(a^(2) + ab + b^(2)), then...

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  9. In a DeltaA B Csum(b+c)tanA/2tan((B-C)/2)=

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  10. In triangle ABC, angleA=pi/3 and b:c =2:3, tan theta=sqrt3/5, 0 lt the...

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  11. In a DeltaABC, AD is the altitude from A. Given b gt c, angleC=23^(@)"...

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  12. If the angles A, B, C (in that order) of triangle ABC are in arithmeti...

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  13. If the radius of the incircle of a triangle withits sides 5k, 6k and 5...

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  14. Two sides of a triangle are 2sqrt2 and 2sqrt3cm and the angle opposite...

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  15. In a triangleABC, a=13cm, b=12 and c=5cm The distance of A from BC is

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  16. In a triangleABC,B=pi/8, C=(5pi)/(8). The altitude from A to the side ...

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  17. In DeltaABC, A = (2pi)/(3), b -c = 3 sqrt3 cm and " area of " Delta AB...

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  18. In DeltaABC if a=(b-c)sectheta then (2sqrt(bc))/(b-c)sin(A/2)=

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  19. In a DeltaABC, (a + b + c) (b + c - a) = lambda bc. (where symbols ha...

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  20. If in DeltaABC, a=2b and A=3B, then A is equal to

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  21. Let the angles A , Ba n dC of triangle A B C be in AdotPdot and let b ...

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