Geometry Problem. Post your solution in the comment box below.
Level: Mathematics Education, High School, Honors Geometry, College.
Details: Click on the figure below.
Tuesday, November 6, 2018
Geometry Problem 1398: Isosceles Triangle, Circle, Radius, Perpendicular, Measurement
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AB = 2^2/1 = 4 = BC
ReplyDeletex = 8^2/BC = 16
But there appears to be something wrong since in the diagram AB + BC < AC
Sumith Peiris
Moratuwa
Sri Lanka
Thanks for your comment. Problem has been updated.
ReplyDeleteProof of updated version, same method
ReplyDeleteAB = d^2/e and BC = f^2/x
Since AB = BC the result follows
Sumith Peiris
Moratuwa
Sri Lanka
f2 =BC*CF = BC*x
ReplyDeleted2 = AE*AB =BC*e
f2/d2 =x/e
x = e * (f2)/(d2)
Florin Popa , Comanesti, Romania
Tangency rule: f^2=x*(x-BF) and d^2=e*(e+EB)
ReplyDeleteBAC is isoscele, therefore: d^2=e*(x-BF)
Dividing side by side:
f^2/d^2=(x*(x-BF))/(e*(x-BF))
Result is: x=e*(f^2/d^2)