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

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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