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prove that cosA +cosB+cosC=1+r/R....

prove that cosA +cosB+cosC=1+r/R.

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PATHFINDER-SOLUTION OF TRIANGLE AND HEIGHT AND DISTANCE-QUESTION BANK
  1. Prove that 1-tan(A/2)tan(B/2)=(2c)/(a+b+c).

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  2. Prove that acosA+bcosB+ccosC=2asinBsinC.

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  3. prove that cosA +cosB+cosC=1+r/R.

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  4. The sides of a triangle are x^2+3x+3,2x+3,x^2+2x. Find the greatest a...

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  5. If P1,P2,P3 be the altitudes of a triangle from the vertices A,B,C Res...

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  6. If in triangleABC ,a^4+b^4+c^4=2c^2(a^2+b^2) then find angleC

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  7. Let h1,h2,h3 be the altitudes of the DeltaABC and let the inradius be ...

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  8. For any triangle ABC, find the value of (bc cos^2(A/2)+cacos^2(B/2)+a...

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  9. If in a DeltaABC, sin^3A+sin^3B+sin^3C=3sinA.sinB.sinC,then find the v...

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  10. AD is a median of the DeltaABC.If AE and AFare medians of the triangle...

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  11. In a triangle DeltaXYZ, let a,b and c be the lengths of the sides opp...

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  12. In a triangle DeltaXYZ, let a, b, and c be the length of the sides opp...

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  13. If the angles of elevation of the top of a water from three collinear ...

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  14. If in a triangle DeltaABC,a^2cos^2A-b^2-c^2=0, then

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  15. In a triangle ABC,angleC=90^@, r and R are the inradius and circumra...

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  16. A bird is sitting on the top of a vertical pole 20 m high and its elev...

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  17. In a DeltaABC, tanA and tanB are the roots of pq(x^2+1)=r^2x. Then Del...

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  18. In a DeltaABC, a,b,c are the sides of the triangle opposite to the ang...

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

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  20. Let p,q,r be the sides opposite to the angles P,Q,R respectively in a ...

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