Geometry Problem 1499. Post your solution in the comment box below.
Level: Mathematics Education, K-12 School, Honors Geometry, College.
Details: Click on the figure below.
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Extend AB to D such that AE = ED
ReplyDeleteNow < CBD = 60, <BDE = 60-2x and so < BED = 60+x = < EBD
Hence DE = BD = AE = BC and so Tr. BCD is equilateral
Therefore, D is the circumcentre of Tr. BCE and so <BCE = 1/2.(<BDE) = 1/2. (60-2x) = 30 - x
But < BCE = 2x and hence 2x = 30 - x from which x = 10
Sumith Peiris
Moratuwa
Sri Lanka
why cbd -60
ReplyDeleteConsider Tr. ABC
Delete<CBD = < A + < C = (60-2x) + 2x = 60
Rgds
Sumith Peiris
very good solution Sumith
ReplyDeleteThank you Peter
DeleteRgds
Sumith
My solution may be found on my blog, https://stanfulger.blogspot.com/2022/11/problem-1499-go-geometry.html
ReplyDeleteHello mathematician can solve my geometry problem?
ReplyDelete