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In triangle $ABC,$ the angle bisector of $\angle BAC$ meets $\overline{BC}$ at $D.$ If $\angle BAC = 60^\circ,$ $\angle CAD = 45^\circ,$ and $AD = 24,$ then find the area of triangle $ABC.$

 Jul 24, 2024
 #1
avatar+280 
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This problem doesn't make sense.

 Jul 29, 2024
edited by BRAINBOLT  Jul 29, 2024
 #2
avatar+1892 
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let me elaborate on what BRAINBOLT said.

 

See, if D lies on the angle bisector of BAC, and angle BAC is 60 degrees, then angle CAD cannot be 45. 

This is because since D lies on the bisector, CAD would therefore be half of BAC, which is 30. 

 

So, this problem is invalid, 

 

Thanks! :)

NotThatSmart  Jul 29, 2024
edited by NotThatSmart  Jul 29, 2024

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