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In the diagram below, triangle ABC is inscribed in the circle and AC = AB . The measure of angle BAC is 42 degrees and segment ED is tangent to the circle at point C. What is the measure of angle ACD?

 

 

codehtml127  Jun 30, 2018
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If AC  = AB ....then triangle  ABC is isosceles....with angles ABC  and ACB  being equal

 

And the measure of angle ABC  = (180 - 42) / 2   =  69°

 

And since angle ABC  is an inscribed angle, then minor arc AC  will  have twice the measure of angle ABC  =  2 * 69  = 138°

 

And since ED is a tangent to the circle at  C, then, by Euclid, angle ACD will have half the measure of minor arc AC  = (1/2)138  =   69°

 

 

cool cool cool

CPhill  Jun 30, 2018

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