# Answer to Question #6620 in Trigonometry for anil jha

Question #6620

properties of triangles.

in the following problem,

In a triangle ABC,if r1 is the exradius of the excircle opposite to A,r2 is the exradius of the excircle opposite to B and r3is the exradius of the excircle opposite to C....

prove that (ar1+br2+cr3)/abc=(1/r)-(1/2R)

where r is the inradius and R is the circum radius.

i tried using these formulae:

r1=(area of triangle)/(s-a)

r1=stanA/2

but i cudnt solve it.how should i start?

in the following problem,

In a triangle ABC,if r1 is the exradius of the excircle opposite to A,r2 is the exradius of the excircle opposite to B and r3is the exradius of the excircle opposite to C....

prove that (ar1+br2+cr3)/abc=(1/r)-(1/2R)

where r is the inradius and R is the circum radius.

i tried using these formulae:

r1=(area of triangle)/(s-a)

r1=stanA/2

but i cudnt solve it.how should i start?

Expert's answer

Dear Anil

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