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

Prove that `cosA+cosB+cosC=1+r/R`

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To prove that \( \cos A + \cos B + \cos C = 1 + \frac{r}{R} \), we can follow these steps: ### Step 1: Start with the expression We begin with the expression we want to prove: \[ \cos A + \cos B + \cos C \] ...
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CENGAGE ENGLISH-PROPERTIES AND SOLUTIONS OF TRIANGLE-Illustration
  1. If the distances of the vertices of a triangle =ABC from the points of...

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

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

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

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

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

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

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

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

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

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

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

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  13. Prove that acosA+bcosB+ccosClt=sdot

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  14. If Delta is the area of a triangle with side lengths a, b, c, then s...

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  15. If in Delta ABC, the distance of the vertices from the orthocenter are...

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  16. ABC is an acute angled triangle with circumcenter O and orthocentre H....

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  17. In a acute angled triangle ABC, proint D, E and F are the feet of the ...

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  18. Prove that the distance between the circumcenter and the orthocentre o...

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  19. Let ABC be an acute angled triangle whose orthocentre is at H. If a...

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  20. In A B C , let L ,M ,N be the feet of the altitudes. The prove that s...

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