Question 577147
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Presume vertex A is the 60 degree angle, then in triangle ACD, angle A is 60 degrees and angle ADC is 90 degrees, so angle ACD must be 30 degrees, therefore triangle ACD is similar to triangle ABC (by Angle-Angle-Angle).  Similarly you can show that triangle BCD is also similar to ABC.


Since in a 30-60-90 right triangle the short leg is one-half of the hypotenuse, AC must be one half of AB and furthermore AD is one half of AC hence AD is one-fourth of AB.  Therefore the ratio of AD to DB is 1/4 to 3/4 which is equivalent to 1:3.


John
*[tex \LARGE e^{i\pi} + 1 = 0]
My calculator said it, I believe it, that settles it
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