Problem: In a circle with center at 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:
Answer Choices:
A. 163r2​
B. 16πr2​
C. 8πr22​​
D. 32r23​​
E. 48r26​​
Solution:
Since AB=r, the measure of angle A is 60 (degrees) and AM=21​r. In right triangle MDA, since AM=21​r and the measure of angle AMD is 30(degrees), AD=41​r and MD=41​r3​.
Therefore, the area of △MDA=21​(AD)(MD)=21​⋅4r​⋅4r3​​=32r23​​.