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If two times the square of the diameter ...

If two times the square of the diameter of the circumcircle of a triangle is equal to the sum of the squares of its sides then prove that the triangle is right angled.

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MOTION-SOLUTION OF TRIANGLE-EXERCISE - 3
  1. Prove that : (r1+r2) tan (C )/(2) = (r3- r) cot ( C)/(2) = c

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  2. Prove that 2R cos A = 2R + r - r(1)

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  3. The triangle ABC is a right angled triangle, right angle at A. The rat...

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  4. The radii r(1), r(2), r(3) of the escribed circles of the triangle ABC...

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  5. Let a, b and c be the sides of a DeltaABC. If a^2, b^2 and c^2 are t...

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  6. If D is the mid point of CA in triangle ABC and Delta is the area of t...

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  7. Show that the radii of the three escribed circles of a triangle are ro...

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  8. If atanA+btanB=(a+b)tan((A+B)/2) prove that triangle ABC is isosceles.

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  9. DEF is the triangle formed by joining the points of contact of the inc...

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  10. DEF is the triangle formed by joining the points of contact of the inc...

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  11. DEF is the triangle formed by joining the points of contact of the inc...

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  12. A cyclic quadrilateral A B C D of areal (3sqrt(3))/4 is inscribed in u...

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  13. If two times the square of the diameter of the circumcircle of a trian...

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  14. In any triangle ABC, if (cos A + 2 cos C)/(cos A + 2 cos B) = (sin B)/...

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  15. The triangle ABC (with side lengths a ,b ,c as usual) satisfies loga^2...

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  16. ABC is a triangle. Circles with radii as shown are drawn inside the tr...

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  17. a, b, c ar the length of sides BC, CA, AB respectively of DeltaABC sa...

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  18. a, b, c ar the length of sides BC, CA, AB respectively of DeltaABC sa...

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  19. If a,b,c are the sides of triangle ABC satisfying log (1 +c/a)+log a -...

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  20. Matching :

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