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A triangle has sides 6,7, and 8. The lin...

A triangle has sides 6,7, and 8. The line through its incenter parallel to the shortest side is drawn to meet the other two sides at P and Q. Then find the length of the segment PQ.

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To solve the problem step by step, we will follow the reasoning and calculations based on the properties of triangles and the relationships between the sides, area, and inradius. ### Step-by-Step Solution: 1. **Identify the sides of the triangle**: We have a triangle with sides \( a = 6 \), \( b = 7 \), and \( c = 8 \). The shortest side is \( a = 6 \). 2. **Calculate the semi-perimeter \( s \)**: \[ ...
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CENGAGE ENGLISH-PROPERTIES AND SOLUTIONS OF TRIANGLE-Illustration
  1. In equilateral triangle ABC with interior point D, if the perpendicula...

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  2. If area of a triangle is 2 sq. units, then find the value of the pr...

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  3. A triangle has sides 6,7, and 8. The line through its incenter para...

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  4. Each side of triangle ABC is divided into three equal parts. Find the ...

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  5. The two adjacent sides of a cyclic quadrilateral are 2a n d5 and the a...

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  6. In triangle A B C ,a : b : c=4:5: 6. The ratio of the radius of the ci...

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  7. Given a triangle A B C with sides a=7, b=8 and c=5. Find the value of ...

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  8. If b=3,c=4,a n dB=pi/3, then find the number of triangles that can be ...

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  9. If A=30^0, a=7,a n db=8 in A B C , then find the number of triangles ...

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  10. If in triangle ABC, (a=(1+sqrt(3))c m ,b=2c m ,a n d/C=60^0 , then fin...

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

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

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

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

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

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

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

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

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

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