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Prove that acosA+bcosB+ccosClt=sdot...

Prove that `acosA+bcosB+ccosClt=sdot`

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To prove that \( a \cos A + b \cos B + c \cos C = s \), we will follow a systematic approach using known properties of triangles and trigonometric identities. ### Step-by-Step Solution: 1. **Start with the given expression**: \[ a \cos A + b \cos B + c \cos C \] ...
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CENGAGE ENGLISH-PROPERTIES AND SOLUTIONS OF TRIANGLE-Illustration
  1. Given a right triangle with /A =90^@. Let M be the mid-point of BC. If...

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

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  3. Prove that acosA+bcosB+ccosClt=sdot

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

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

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

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

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

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

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

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  11. The lengths of the medians through acute angles of a right-angled tr...

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  12. Two medians drawn from acute angles of a right angled triangles inters...

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

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  14. If in a triangle r1=r2+r3+r , prove that the triangle is right angled.

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  15. Prove that (r(1+r2))/1=2R

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  16. Prove that (r+r1)tan((B-C)/2)+(r+r2)tan((C-A)/2)+(r+r3)tan((A-B)/2)=0

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  17. If the distance between incenter and one of the excenter of an equi...

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  18. If I(1), I(2), I(3) are the centers of escribed circles of Delta ABC, ...

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  19. Prove that the sum of the radii of the radii of the circles, which are...

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  20. If the area of the circle is A1 and the area of the regular pentagon i...

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