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If r and R are radii of the incircle and...

If r and R are radii of the incircle and circum-circle of `DeltaABC, ` then prove that :
`8rR{cos ^(2) A//2 +cos ^(2) B//2 +cos ^(2) C//2}`
`=2bc+2ca+2ab-a^(2) -b^(2) -c^(2).`

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The correct Answer is:
`8rR{cos ^(2) A//2+cos ^(2) B//2 +cos ^(2) C//2}=2bc+ 2ab+2ca-a^(2)-b^(2) -c^(2)`
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ARIHANT MATHS-PROPERTIES AND SOLUTION OF TRIANGLES -Exercise (Questions Asked In Previous 13 Years Exam)
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  2. Prove that 2sin^2(pi/6) - sec^2(pi/3)= -7/2

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  3. In a triangle the sum of two sides is x and the product of the same is...

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  4. Consider a triangle A B C and let a , b and c denote the lengths of th...

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  5. Solution of differential equation 2xy dy / dx = x^2 + 3y^2 is .

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  6. Let PQR be a triangle of area Delta with a = 2, b = 7//2, and c = 5//2...

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  7. If the angle A ,Ba n dC of a triangle are in an arithmetic propression...

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  8. Let A B C be a triangle such that /A C B=pi/6 and let a , b and c deno...

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  9. A triangle A B C with fixed base B C , the vertex A moves such that co...

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  10. Let A B Ca n dA B C ' be two non-congruent triangles with sides A B=4,...

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  11. A straight line through the vertex P of a triangle P Q R intersects th...

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  12. Consider the circle x^2 + y^2 = 9 and the parabola y^2 = 8x. They inte...

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  13. Consider the circle x^2 + y^2 = 9 and the parabola y^2 = 8x. They inte...

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  14. Consider the circle x^2 + y^2 = 9 and the parabola y^2 = 8x. They inte...

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  15. Internal bisector of /A of triangle ABC meets side BC at D. A line dra...

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  16. One angle of an isosceles triangle is 120^0 and the radius of its incr...

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  17. In Delta ABC, which one is true among the following ?

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  18. Let a vertical tower A B have its end A on the level ground. Let C be ...

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  19. ABCD is a trapezium such that AB and CD are parallel and BC bot CD. If...

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  20. For a regular polygon, let r and R be the radii of the inscribed and t...

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  21. In triangle A B C , let /c=pi/2dot If r is the inradius and R is circu...

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