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

ReplyDelete