MHB Find Length X in Triangle: Learn How to Calculate It

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The discussion centers on calculating the length x in a triangle where FH and HC are perpendicular. Participants express confusion about the problem and seek clarification on the relationships between the triangle's components. A hint is provided regarding the similarity of triangles, suggesting that identifying similar triangles can lead to the solution. The calculation involves the ratio x = 4 * CF / BF, which helps in finding the length. The conversation highlights the importance of understanding triangle properties to solve the problem effectively.
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what is the length x? (FH and HC perpendicular too, which I missed to write)
I am totally stuck can not make any progress on this question. Answer should be 5. I don't know how to obtain it

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ketanco said:
FH and HC perpendicular too
Does that mean that angleCHF = 90?
Your writing is terrible!
AB = 9 and EF = 4?

Not important but why is there no point G (you jumped from F to H!)
 
ketanco said:
what is the length x? (FH and HC perpendicular too, which I missed to write)
I am totally stuck can not make any progress on this question. Answer should be 5. I don't know how to obtain it

Hint: Which triangles are similar to each other?
(Two triangles are similar if they have 2 angles in common.)
 
Once you get Klaas' hint, you should "see" that x = 4 * CF / BF
 

Thread 'Trigonometry problem of interest'

Seemingly by some mathematical coincidence, a hexagon of sides 2,2,7,7, 11, and 11 can be inscribed in a circle of radius 7. The other day I saw a math problem on line, which they said came from a Polish Olympiad, where you compute the length x of the 3rd side which is the same as the radius, so that the sides of length 2,x, and 11 are inscribed on the arc of a semi-circle. The law of cosines applied twice gives the answer for x of exactly 7, but the arithmetic is so complex that the...
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