A rectangle, HOMF, has sides HO=11 and OM=5. A triangle ABC has H as orthocentre, O as circumcentre, M be the midpoint of BC, F is the foot of altitude from A. What is the length of BC?
https://www.desmos.com/geometry/7ksviraeka
BC=28
I put O=(0,0), H=(11,0), M=(0,5), F=(11,5)
B and C must be in line with M and F so with parameter b we have
B=(-b,5), C=(b,5) and seek to find 2b.
BA must have a slope perpendicular to CH
CA must have a slope perpendicular to BH
A must be the intersections on the lines given in eq 10 & 11
A coordinates in eq 15.
Line through O and the midpoint of AC must be perpendicular to AC.
This is eq 16-19. So b=14 and 2b=BC=28.
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Posted by Jer
on 2024-10-14 17:53:17 |
Coordinate solution