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O is the circumcenter of A B Ca n dR1, ...

`O` is the circumcenter of ` A B Ca n dR_1, R_2, R_3` are respectively, the radii of the circumcircles of the triangle `O B C ,O C A` and OAB. Prove that `a/(R_1)+b/(R_2)+c/(R_3)=(a b c)/(R_3)`

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To prove that \[ \frac{a}{R_1} + \frac{b}{R_2} + \frac{c}{R_3} = \frac{abc}{R^3} \] where \( O \) is the circumcenter of triangle \( ABC \) and \( R_1, R_2, R_3 \) are the circumradii of triangles \( OBC, OCA, \) and \( OAB \) respectively, we can follow these steps: ...
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CENGAGE ENGLISH-PROPERTIES AND SOLUTIONS OF TRIANGLE-Illustration
  1. In A B C ,s i d e sb , c and angle B are given such that a has two va...

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  2. In A B C ,a , ca n dA are given and b1,b2 are two values of the third...

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

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  4. In A B C ,C=60^0a n dB=45^0dot Line joining vertex A of triangle and ...

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  5. The diameters of the circumcirle of triangle ABC drawn from A,B and C ...

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  6. Find the lengths of chords of the circumcircle of triangle ABC, made b...

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  7. Let A B C be a triangle with /B=90^0 . Let AD be the bisector of /A wi...

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  8. If the distances of the vertices of a triangle =ABC from the points of...

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  9. If x , ya n dz are the distances of incenter from the vertices of the ...

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  10. Prove that cosA+cosB+cosC=1+r/R

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  11. Prove that ("a c o s"A+b cosB+ccosC)/(a+b+c)=r/Rdot

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  12. Incircle of A B C touches the sides BC, CA and AB at D, E and F, resp...

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  13. In an acute angled triangle A B C , a semicircle with radius ra is con...

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  14. Let the incircle with center I of A B C touch sides BC, CA and AB at ...

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  15. In A B C , the bisector of the angle A meets the side BC at D andthe ...

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  16. Let I be the incetre of ΔABC having inradius r. Al, BI and Ci intersec...

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  17. In A B C , the three bisectors of the angle A, B and C are extended t...

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  18. Given a right triangle with /A =90^@. Let M be the mid-point of BC. If...

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  19. Prove that the distance between the circumcenter and the incenter of ...

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  20. Prove that acosA+bcosB+ccosClt=sdot

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