Math CentralQuandaries & Queries


Question from Anonymous, a student:

An equilateral triangle with sides 6 inches is inscribed in a circle. What is the diameter of the circle?


By the symmetry in my diagram the measure of angle $BCA$ is $\frac{360}{3} = 120$ degrees. The sum of the measures of the angles of a triangle is $180^o$ and hence the measure of angle $CAB$ is $30^o$.

circle and triangle

D is the midpoint of $BA$ and hence angle $ADC$ is a right angle. Do you see why? What trig function relates the measure of angle $CAD$ to the lengths of $CA$ and $AD?$


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