# Length of BC

#### caffeinemachine

##### Well-known member
MHB Math Scholar
Hello Albert,

In the above problem can you please clarify if E lies on BC or not? If not, then how is E defined other than than AE=10.

#### Albert

##### Well-known member
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
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
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 ?

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#### caffeinemachine

##### Well-known member
MHB Math Scholar
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
yes,you got it 