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In the diagram below, triangle $ABC$ is inscribed in the circle and $AC = AB$. The measure of angle $BAC$ is $30$ degrees and segment $ED$ is tangent to the circle at point $C$. What is the measure of angle $ACD$?

 

 Jan 2, 2024
 #1
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Since AB  = AC and BAC = 30

 

Then angle  ACB = (180 -30) / 2  = 75

 

And since BAC = 30.....then  minor arc BC = 60...so  angle BCE = (1/2)(60) = 30

 

So angle ACD  =180  - BCE - ACB   = 180  - 75 - 30 =  75°

 

 

cool cool cool

 Jan 3, 2024

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