June 6th, 2019, 08:17 PM  #1 
Newbie Joined: Jun 2019 From: New York Posts: 2 Thanks: 0  Help with proof?
The givens are, Quad ABCD is inscribed inside the circle Diagonals AC and BD meet at point E. Line AD is congruent to Line CD How do you prove that BE * AD = EC * AB? 
June 7th, 2019, 12:49 AM  #2 
Global Moderator Joined: Dec 2006 Posts: 20,969 Thanks: 2219 
$\small\angle$ADB = $\small\angle$ACB = $\small\angle$ECB and $\small\angle$ABD = $\small\angle$DBC = $\small\angle$EBC. AB/AD = sin($\small\angle$ADB)/sin($\small\angle$ABD) = sin($\small\angle$ECB)/sin($\small\angle$EBC) = BE/EC. 

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