Prove AB=2CE | Geometry Problem

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To prove that AB=2CE, start by calculating the angles of triangle CDE in terms of angle BAC, given that line AC is parallel to DE. Use the sine formula to establish a relationship between the lengths |CE| and |CD|. The varying angle BAC will affect the angles of triangle CDE, but they remain interrelated. This relationship allows for the necessary proof to be constructed. The discussion emphasizes the importance of understanding angle relationships in geometry.
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In the figure attached, I have to prove AB=2CE given that: line AC is parallel to DE and angles as mentioned in the figure. Can anyone please help me to prove the same?
 

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Calculate angles of the triangle ##CDE## in terms of ##\angle BAC## Then use the sine formula to relate ##|CE|## to ##|CD|##
 
∠BAC can vary and so will the angles of the Triangle CDE
 
rushikesh said:
∠BAC can vary and so will the angles of the Triangle CDE

They can. But they're related, so you can express one in terms of the other.
 

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