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Let triangle ABC have centroid G. D lies on AB such that AD/BD=2/3, and E lieson AC such that AE/CE =4/5. Lines DG and EG intersect BC at points P and Q, respectively. Find PQ/BC.

 Jul 3, 2021
 #1
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By mass points, PQ/BC = 5/13.

 Jul 3, 2021
 #2
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can you elaborate?

Guest Jul 3, 2021
 #3
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Let triangle ABC have centroid G. D lies on AB such that AD/BD=2/3 and E lie on AC such that AE/CE =4/5. Lines DG and EG intersect BC at points P and Q, respectively. Find PQ/BC.

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I used an equilateral triangle and the answer is: PQ / BC = 7 / 12

 

Here's my work laugh

 Jul 3, 2021
 #4
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how did you get the angles

Guest Jul 3, 2021
 #5
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ABC is an equilateral triangle with the length of a side of 45 (45 is evenly divisible by 5 and 9)

 

Point G is the centroid, so the length of AG = 2/3(AN)

 

Use AD, AE, and angle EAG to calculate the angles.

Guest Jul 5, 2021

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