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Length of BC

Albert

Well-known member
Jan 25, 2013
1,225
Find length of BC:

Find length  of BC.jpg
 

caffeinemachine

Well-known member
MHB Math Scholar
Mar 10, 2012
834

Albert

Well-known member
Jan 25, 2013
1,225
Point E is on angle bisector of angle A, and AE=10

E is not on BC (from the diagram given)
 

caffeinemachine

Well-known member
MHB Math Scholar
Mar 10, 2012
834
Point E is on angle bisector of angle A, and AE=10

E is not on BC (from the diagram given)
But then I think BC doesn't have a unique length. Take BC =16 and the mid point of BC be D. Point E is on the side of BC different from that of A and ED=2 with ED perpendicular to BC. In fact any value of BC>16 can provide a configuration confirming to the hypothesis if the question.
 

Albert

Well-known member
Jan 25, 2013
1,225
yes, the length of BC is not unique ,it depends on how student draw the diagram

sometimes we plot an open problem ,and want to test the abilities of students in analyzing

now using the diagram given if I said BC=$\dfrac {50}{3}$

what wiil be the sum of the three side lengths of triangle ABC ?
 
Last edited:

caffeinemachine

Well-known member
MHB Math Scholar
Mar 10, 2012
834
yes, the length of BC is not unique ,it depends on how student draw the diagram

sometimes we plot an open problem ,and want to test the abilities of students in analyzing

now using the diagram given if I said BC=$\dfrac {50}{3}$

what wiil be the sum of the three side lengths of triangle ABC ?
$10$ and $40/3$. Is this correct?
 

Albert

Well-known member
Jan 25, 2013
1,225
yes,you got it :)