smc

Question

In a circle with center O and radius r, chord AB is drawn with length equal to r (units). From O, a perpendicular to AB meets AB at M. From M a perpendicular to OA meets OA at D. In terms of r the area of triangle MDA, in appropriate square units, is:

Accepted Answer

FIGURE Because AO = OB = AB, AOB is an equilateral triangle, and OAB = 60^. Using 30-60-90 triangles, AM = r2, AD = r4, and DM = r34. Thus, the area of ADM is 12 r4 r34 = r^2332.