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In A B C , if r\ : r1: R=2\ : 12\ :5, w...

In ` A B C` , if `r\ : r_1: R=2\ : 12\ :5,` where all symbols have their usual meaning, then ` A B C` is an acute angled triangle ` A B C` is an obtuse angled triangle ` A B C` is right angled which is not isosceles ` A B C` is isosceles which is not right angled

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ALLEN-SOLUTION AND PROPERTIES OF TRIANGLE-All Questions
  1. With usual notations in a triangle A B C , if r1=2r2=2r3 then 4a=3b (b...

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  2. a, b, x are in A.P., a,b,y are in G.P. and a, b, z are in H.P. then:

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  3. In A B C , if r\ : r1: R=2\ : 12\ :5, where all symbols have their us...

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  4. If a , b ,\ A are given in a triangle and c1a n d\ c2 are two possible...

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  5. If cos A+cos B+2cos C=2 then the sides of the A B C are in A.P. (b) G...

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  6. In a triangle A B C ,\ C D is the bisector of the angle Cdot If cosC/2...

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  7. The medians of a A B C are in 9c m ,\ 12 c m\ a n d\ 15 c m respectiv...

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  8. If ' O ' is the circum centre of the A B C and R1,\ R2,\ R3 are the r...

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

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

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

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  13. Prove that : 4\ R\ sin AsinB\ sin C=acosA+b\ cos B+c cosCdot

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  14. If p1,\ p2, p3 are the altitudes of a triangle from the vertices A , B...

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  15. For any triangle ABC, If B=3C, show that cosC=sqrt((b+c)/(4c)) and s...

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  16. A B C is a triangle. D is the mid point of B Cdot If A D is perpendicu...

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  17. Prove that r1+r2+r3-r=4R

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  19. In a DeltaABC, the median to the side BC is of length 1/sqrt(11-6sqrt...

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  20. Prove that : (r1)/(b c)+(r2)/(c a)+(r3)/(a b)=1/r-1/(2R)

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