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Let's solve together

HELLO EVERYONE,
I am a 15 years old boy from Bangladesh,who has always loved doing GEOMETRY and probably would be,always.Actually,i am quite insistent to find the solution of any problem.Even I solved some of them after trying several months continuously!! However,here I would like to introduce a Geometry Problem that I have been trying for about 3 months but haven't found much clue.WHY DON'T SOLVE TOGETHER?!


In the diagram above,▲ADB is a right angled triangle,where ∠ADB is right angle.E is a point on DB.EF is perpendicular to AB.AE meets the circumcircle of ▲ADB at H and FH meets DB at G.Given that. DE=5,EG=3.Find the value of BG.
All I have found is some similar triangles, even adding something new seemed more complex.I will of course share ,what I have found this far.lets discuss together! You can share any of your thoughts regarding the problem and ask any question freely!! HOPE TO TALK TO YOU SOON! ;))

Note by Shamin Yeaser
2 weeks ago

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BG=12

Hint: Drop the altitude from D onto AB and extend to intersect with circumcircle. Compare with the point of intersection of FH with the circumcircle(on the other side).

Maria Kozlowska - 1 week, 5 days ago

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OH MY GOD!!! You even don't know,how much emotions I gathered around this math.I thought for a moment,if I would be able to solve that ever or not.THANK YOU SO MUCH!!! I tried by the method, and found that they both meet at the same point.then I worked with the similar triangles!! again,than you!! Your favor truly means a lot to me. gonna follow you now. ;))

Shamin Yeaser - 1 week, 5 days ago

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