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In an equilateral triangle, the inradius...

In an equilateral triangle, the inradius, circumradius, and one of the exradii are in the ratio

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ALLEN-SOLUTION AND PROPERTIES OF TRIANGLE-All Questions
  1. In triangle A B C where A ,\ B ,\ C are acute, the distances of the or...

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  2. In a Delta ABC, show that (a cos A+b cos B+ c cos C)/(a+b+c)= (r )/(R...

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  3. In an equilateral triangle, the inradius, circumradius, and one of the...

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  4. Show that ((1)/(r (1))+ (1)/(r(2)))((1)/(r(2))+(1)/(r (3)))((1)/(r (3)...

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  5. In a triangle A B C ,(r1+r2)/(1+cosC) is equal to (2a b)/(c"Delta") (b...

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  6. With usual notations in a triangle A B C , if r1=2r2=2r3 then 4a=3b (b...

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  7. If r1,\ r2a n d\ r3 be the radii of excircles of the triangle A B C , ...

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

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

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  10. If a,b A be given in a triangl and c(1) and c(2) two possible values o...

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  11. If A , B , C are angles of a triangle which of the following will not ...

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  12. In a A B C , S/R is equal to s in A+s in B+s in C (b) 4cosA/2cosB/2co...

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

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  14. The line x/6+y/8=1 cuts the co-ordinate axis at A\ &\ B . If O is orig...

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

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

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

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

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

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

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