Calculating the Length of BC: A Geometric Exploration

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Discussion Overview

The discussion revolves around calculating the length of segment BC in a geometric configuration involving point E, which lies on the angle bisector of angle A. The problem explores the implications of the placement of E and the resulting configurations of triangle ABC.

Discussion Character

  • Exploratory
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • Some participants seek clarification on whether point E lies on segment BC, which affects the definition of the problem.
  • It is noted that E is on the angle bisector of angle A and is not on BC, with AE defined as 10.
  • One participant suggests that BC does not have a unique length, proposing that any value greater than 16 could satisfy the conditions of the problem.
  • Another participant agrees that the length of BC is not unique and emphasizes that it depends on how the diagram is drawn by the student.
  • A specific example is given where BC is set to $\dfrac{50}{3}$, prompting a question about the sum of the side lengths of triangle ABC.
  • Participants engage in verifying the correctness of the side lengths based on the proposed value of BC.

Areas of Agreement / Disagreement

Participants generally agree that the length of BC is not unique and depends on the diagram's construction. However, there is no consensus on a specific value or configuration that satisfies the problem's conditions.

Contextual Notes

The discussion highlights the dependence on the diagram's interpretation and the assumptions made regarding the placement of points in the geometric configuration.

Albert1
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Albert said:
Find length of BC:

View attachment 708
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.
 
Point E is on angle bisector of angle A, and AE=10

E is not on BC (from the diagram given)
 
Albert said:
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.
 
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:
Albert said:
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?
 
yes,you got it :)
 

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