MHB Finding $\angle ADC$ in $\triangle ABC$

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In triangle ABC, with AB equal to AC and an inner point D such that AB, AC, and BD are equal, the problem seeks to find angle ADC given that angle DCB is 30 degrees. The discussion revolves around solving for angle ADC using the properties of isosceles triangles and the given angle. Participants express varying levels of difficulty with the problem, indicating it may serve as a challenge for some members. The solution requires applying geometric principles to derive the desired angle. Ultimately, the focus is on finding angle ADC based on the established conditions.
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$\triangle ABC, \overline{AB}=\overline {AC}$,there exists an inner point ${D}$ and satisfyng :
(1)$\overline {AB}=\overline {AC}=\overline {BD}$
(2)$\angle DCB=30^o$
find $\angle ADC=?$
 
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Are these problems you need help with? Or are they just for members to try?
 
Joppy said:
Are these problems you need help with? Or are they just for members to try?

for members to try
 
Albert said:
$\triangle ABC, \overline{AB}=\overline {AC}$,there exists an inner point ${D}$ and satisfyng :
(1)$\overline {AB}=\overline {AC}=\overline {BD}$
(2)$\angle DCB=30^o$
find $\angle ADC=?$
my solution
explanation :
GD//BC
let DE=GH=1,
EF=FH=x,
AK=y
$\angle DEC=\angle GHB=90^o$
Triangle AGD is an equilateral triangle

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