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D , E , F are the foot of the perpendicu...

`D , E , F` are the foot of the perpendicular from vertices `A , B , C` to sides `B C ,\ C A ,\ A B` respectively, and `H` is the orthocentre of acute angled triangle `A B C` ; where `a , b , c` are the sides of triangle `A B C` , then `H` is the incentre of triangle `D E F` `A , B ,\ C` are excentres of triangle `D E F` Perimeter of ` D E F` is `a cos A+b cos B+c\ cos C` Circumradius of triangle `D E F` is `R/2,` where `R` is circumradius of ` A B C`

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D , E ,a n dF are the middle points of the sides of the triangle A B C , then (a) centroid of the triangle D E F is the same as that of A B C (b) orthocenter of the tirangle D E F is the circumcentre of A B C

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ALLEN-SOLUTION AND PROPERTIES OF TRIANGLE-All Questions
  1. The line x/6+y/8=1 cuts the co-ordinate axis at A\ &\ B . If O is orig...

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  2. In triangle ABC, CD is the bisector of the angle C. if cos.(C)/(2) = (...

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  3. D , E , F are the foot of the perpendicular from vertices A , B , C to...

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  4. In an isosceles A B C , the altitudes intersect on the inscribed circ...

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  5. In a triangle ABC cos^(2)A/2+cos^(2)B/2+cos^(2)C/2=

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  6. If in a triangle A B C\ p ,\ q ,\ r are the altitudes from the vertice...

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  7. A D ,\ B E\ A N D\ C F are the perpendiculars from the angular points ...

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

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  9. In a triangle A B C ,\ (r1-r)(r2-r)(r3-r) is equal to 4R r^2 (b) (4a b...

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  10. Two rays emanate from the point A and form an angle of 43 with one a...

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  11. In a A B C ,\ A=pi/3\ a n d\ b : c=2: 3. If tanalpha=(sqrt(3))/5,\ o<...

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  12. In A B C , on the side B C ,D and E are two points such that B D=D E=...

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  13. In a A B C ,\ A D is the bisector of the angle A meeting B C at Ddot ...

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  14. If p1, p2, p3, be the altitudes of a triangle ABC from the vertices A,...

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  15. The value of (cosA)/(P1)+(cosB)/(P2)+(cosC)/(P3) is

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  16. The minimum value of (b^2p1)/c+(c^2p2)/a+(a^2p3)/b\ is

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  17. Find the value of a if the value of 2x^2+3x-a is equal to 6 when x=-2.

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  18. Statement - I : If two sides of a triangle are 4 and 5, then its ar...

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  19. Statement I perimeter of a regular pentagon inscribed in a circle with...

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  20. Statement - I : The statement that circumradius and inradius of a t...

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